Conference abstracts

Keynote talks

Maria Cameron

Theory and Computation of the Quasipotential

Many processes in nature e.g. genetic switches, ecological systems, and nonlinear oscillators with periodic forcing can be modeled using stochastic differential equations (SDEs) with small noise. For gradient SDEs, the invariant probability measure and the most probable escape paths from the attractors can be expressed in terms of their potential functions. For nongradient SDEs, the counterpart of the potential function is the quasipotential, a key function in the large deviations theory (Freidlin and Wentzell, 1970s — 2010s). The quasipotential is a function defined on the phase space as the solution to a certain optimal control problem. It allows us to obtain asymptotic estimates for the invariant measure in the small noise limit, find the most probable escape paths, and facilitate the visualization of the stochastic dynamics. I will give an overview of the theory of the quasipotential and discuss two approaches to computing it in whole regions of the phase space. The first approach is based on a greedy algorithm for solving a certain optimal control problem on the mesh in the phase space. The second approach directly computes the Lagrangian manifold in the lifted space and then projects the quasipotential level sets to the phase space.

Bartłomiej Dybiec

Metastability and Jump Processes

A particle immersed in a liquid constantly interacts with other particles. Due to the enormous number of collisions, these interactions cannot be described exactly. An effective approximate description is provided by noise. Noise is a stochastic process that is used to describe complicated or not fully known interactions. According to central limit theorems, the sum of many independent identically distributed random variables tends to the Gaussian distribution (if components are characterized by finite variance) or to the α-stable density (diverging variance of components). Consequently, the Lévy noise and its special case—the Gaussian white noise (GWN)—are frequently used in the description of noise driven systems in the out-of-equilibrium and equilibrium regimes, respectively. Both of them share numerous similarities, however they significantly and inherently differs. α-stable noises (with α < 2) inevitably lead to occurence of long jumps. Increasing number of observations demonstrates a plethora of situations in which non-Gaussian heavy tailed fluctuations are recorded. This indicates the need to include heavy-tailed fluctuations in the description of dynamical systems especially in out-of-equilibrium realms. The possibility of anomalously long jumps, drastically changes the properties of stochastic dynamical systems compared to their Gaussian noise driven counterparts. It is the long jumps that lead to bimodal non-equilibrium stationary states in single-well, super-harmonic, potential wells. Exploration of different scenarios for restricting or eliminating long jumps, allows for a better understanding of how long jumps determine the properties of stationary states and how they affect their modality. This provides a deeper understanding of the role of non-Gaussian long jumps and the mechanisms responsible for emergence of multimodal stationary states.

Steve Fitzgerald

Path Integrals and Stochastic Transitions

Traditionally, stochastic processes are modelled using either a Fokker-Planck PDE approach, or a Langevin SDE approach. There is also a third way: the functional or path integral. Originally developed by Wiener in the 1920s to model Brownian motion, path integrals were famously applied to quantum mechanics by Feynman in the 1950s. However, they also offer much to classical stochastic processes. In this talk I will introduce the formalism, focussing on the dominant contribution to the path integral when the noise is weak. There exists a remarkable correspondence between the most-probable stochastic paths and Hamiltonian mechanics in an effective potential [1,2,3]. I will then discuss applications, including reaction pathways conditioned on finite time [2]. We demonstrate that the most probable pathway may be very different from the usual minimum energy path used to calculate the average reaction rate. If time permits, I will also discuss the extremely nonlinear crystal dislocation response to applied stress [4].

Tobias Grafke

Metastability and rare transitions via sharp large deviation estimates

Metastability in complex systems manifests in long periods of continued presence in a collection of states of the system, interspersed by rare and rapid transitions between them. Predicting the nature and likelihood of these rare transitions is hard because of the their low probability and associated long waiting times. Large deviation theory provides a classical way of dealing with events of extremely small probability, but generally only yields the exponential tail scaling of rare event probabilities. In this talk, I will discuss theory, and algorithms based upon it, that improve on this limitation, yielding sharp quantitative estimates of rare event probabilities from a single computation and without fitting parameters. The applicability of this method to high-dimensional real-world systems, for example coming from fluid dynamics or molecular dynamics, are discussed.

Aneta Koseska

Emergence of quasi-stability in biological systems

A growing body of empirical evidence suggests that neuronal and biochemical networks are often characterized by long transients which are quasi-stable, with fast switching between them. The duration of the quasi-stable patterns is much longer than one would expect from the characteristic elementary processes of the system, whereas the switching is triggered by external signals or system-autonomously, and occurs on a timescale much shorter than the one of the preceding dynamical pattern. Generalizing the concept of ghost states, we provide a theoretical framework that accounts for emergence of transiently stable phase-space flows generated by ghost scaffolds. We demonstrate that ghost-based phase space objects such as ghost channels and cycles account for emergence of advanced information processing capabilities, including on-the-fly signal classification, temporal integration and context-dependent responses.

Ying-Cheng Lai

Global phase-space approach to rate-induced tipping in complex biological networks

In ecosystems, environmental changes as a result of natural and human processes can cause some key parameters to change with time. Depending on how fast such a parameter changes, a tipping event can occur. Existing works on rate-induced tipping, or R-tipping, provided mathematical insights into this phenomenon in low-dimensional systems from a local dynamical point of view, revealing, e.g., the existence of a critical rate for some specific initial condition above which tipping will occur. Motivated by the observation that ecosystems are dynamic, most likely transient, and constantly driven away from some equilibrium state, we develop a global phase-space approach to R-tipping. In particular, we introduce the notion of the probability of R-tipping defined for initial conditions in the phase space. Using real-world, complex high-dimensional mutualistic networks as a paradigm, we discover a scaling law between this probability and the rate of parameter change, and provide a geometric theory to explain the scaling. Our analysis elucidates the meaning of the critical rate and its dependence on initial conditions. The phase-space approach offers a comprehensive physical framework to understand R-tipping.

This is a joint work with Dr. Shirin Panahi from Arizona State University, Prof. Younghae Do from Kyungpook National University in South Korea, and Prof. Alan Hastings from UC Davis.

Kathrin Padberg-Gehle

Metastability and almost-invariant sets (cancelled)

Metastability and almost-invariant sets are key concepts in the study of dynamical systems as they determine the long-term behavior of complex systems. An almost-invariant set is a subset of state space are characterized by the property that trajectories starting in it have a high probability of remaining in the set over a significant time duration. We will discuss numerical methods for the identification and characterization of almost-invariant sets and also address data-based and nonautonomous extensions. All approaches are demonstrated in a number of example systems, including turbulent Rayleigh-Bénard convection.

Reyk Börner

Melancholia State of Metastable Ocean Currents and its Role for Critical Transitions

Replacement talk for Kathrin Padberg-Gehle

Grigorios A. Pavliotis

Phase Transitions and Dynamical Metastability for Stochastic Interacting Particle Systems

We consider systems of weakly interacting diffusions on the torus. In the mean field limit, the dynamics is described by the McKean-Vlasov PDE. We show that for interaction potentials that are not H-stable, we have non-uniqueness of stationary states, e.g. phase transitions at low temperatures. Furthermore, we show that for sufficiently short-range attractive interaction potentials, the phase transition is discontinuous. We then show that stochastic interacting particle systems that exhibit discontinuous phase transitions exhibit dynamical metastability and clustering. We finally show that the dynamics of the emergent clusters can be described using a system of coalescing Brownian motions.

Sergei Petrovskii

Long Transients as a Possible Mechanism of Regime Shifts and Metastable Dynamics in Ecosystems

Ecological systems often show abrupt, significant changes - regime shifts - in response to apparently small, gradual changes in environmental conditions. Moreover, sometimes a regime shift happens without any clear reasons at all. Growing empirical evidence eventually led to a mathematical concept of tipping points [1]. In particular, B-tipping links an abrupt change to a bifurcation, e.g. to a saddle-node bifurcation resulting in a disappearance of a stable steady state. A few different types of tipping mechanisms have been suggested such as N-tipping (transitions in a multi-well potential due to the effect of noise), R-tipping (transitions due to a high rate of change) and P-tipping (extreme sensitivity during certain phases of system’s dynamics, cf. [2]). In my talk, I will discuss an alternative, different mechanism that can result in metastable dynamics: long transients [3]. During long transient dynamics, the system can mimic a possible asymptotical regime (e.g., steady state, limit cycle, or chaos) over an indefinitely long yet finite period of time before undergoing a fast transition to a different regime. There is a variety of mathematical structures that can lead to long transient dynamics, such as ‘crawlbys’, ghost attractors, slow-fast timescales, etc. [3,4]. I will emphasize the relation between long transients and metastability and argue that such “LT-tipping” is a plausible alternative to other types of tipping, in particular as it does not necessarily require presumptions needed for other types of tipping to occur.

Larissa Serdukova

Lévy-noise versus Gaussian-noise-induced Transitions in the Ghil-Sellers Energy Balance Model

We study the impact of applying stochastic forcing to the Ghil–Sellers energy balance climate model in the form of a fluctuating solar irradiance. Through numerical simulations, we explore the noise-induced transitions between the competing warm and snowball climate states. We consider multiplicative stochastic forcing driven by Gaussian and α stable Lévy – α ∈ (0,2) – noise laws, examine the statistics of transition times, and estimate the most probable transition paths. While the Gaussian noise case – used here as a reference – has been carefully studied in a plethora of investigations on metastable systems, much less is known about the Lévy case, both in terms of mathematical theory and heuristics, especially in the case of high- and infinite-dimensional systems. In the weak noise limit, the expected residence time in each metastable state scales in a fundamentally different way in the Gaussian vs. Lévy noise case with respect to the intensity of the noise. In the former case, the classical Kramers-like exponential law is recovered. In the latter case, power laws are found, with the exponent equal to −α, in ap parent agreement with rigorous results obtained for additive noise in a related – yet different – reaction–diffusion equation and in simpler models. This can be better understood by treating the Lévy noise as a compound Poisson process. The transition paths are studied in a projection of the state space, and remarkable differences are observed between the two different types of noise. The snowball-to-warm and the warm-to-snowball most probable transition paths cross at the single unstable edge state on the basin boundary. In the case of Lévy noise, the most probable transition paths in the two directions are wholly separated, as transitions apparently take place via the closest basin boundary region to the outgoing attractor. This property can be better elucidated by considering singular perturbations to the solar irradiance.

Contributed talks

Day 1 - Tuesday

Transient metastability and apparent tipping in discrete-time models of population dynamics

Andrew Morozov, University of Leicester
Tuesday, 16:40-17:00, Room 3

Traditionally, mathematical models in ecology were focused on long-term, asymptotic behaviour of ecosystems. However, recently, there has been a growing appreciation of the role of transients, in particular, long transients, both in empirical ecology and theoretical studies. Many models predict that a system can function for a long time in a certain state (a ‘quasi-stable regime’), and, later, can exhibit a fast transition to another regime. This scenario is understood as transient metastability, where apparent tipping occurs without underlying proximal source of a regime shift, or alteration of the system could have occurred long ago before the transition. Transients-related metastability provides an alternative explanation to the classical regime shift paradigm based on tipping points. In this study, we investigate patterns of long transients and transient-related regime shifts occurring in time-discrete population models, which are mathematically described by discontinuous (piece-wise) maps. The particularity of the considered models is that they incorporate density-dependent dispersal of species. We demonstrate transients due to crawl-by dynamics, chaotic repellers, chaotic saddles, ghost attractors, and a rich variety of intermittent regimes. We explore the space of key model parameters and show that long transients are omnipresent since they can be observed within a wide range of model parameters. We also reveal the possibility of a cascade of transient metastability regimes with multiple switching between quasi-stable dynamics. We also considered a stochastic version of the model, where some parameters exhibit random fluctuations. We conclude that the discontinuity in population models significantly facilitates the emergence of long transients by creating new types and increasing parameter domains of the corresponding transient dynamics. Another important conclusion is that the asymptotic regime of population dynamics is hardly possible to predict based on a finite time course of species densities, which is crucial for ecosystem management and decision making.

Dynamical properties and mechanisms of metastability: a perspective in neuroscience

Kalel Luiz Rossi, University of Oldenburg
with Roberto C. Budzinski, Everton S. Medeiros, Bruno R.R. Boaretto, Lyle Muller, Ulrike Feudel
Tuesday, 17:00-17:20, Room 3

Metastability, characterized by a variability of regimes in time, is a ubiquitous type of neural dynamics. It has been formulated in many different ways in the neuroscience literature, however, which may cause some confusion. In this work, we discuss metastability from the point of view of dynamical systems theory. We extract from the literature a very simple but general definition through the concept of metastable regimes as long-lived but transient epochs of activity with unique dynamical properties. This definition serves as an umbrella term that encompasses formulations from other works, and readily connects to concepts from dynamical systems theory. This allows us to examine general dynamical properties of metastable regimes, propose in a didactic manner several dynamics-based mechanisms that generate them, and discuss a theoretical tool to characterize them quantitatively. This work leads to insights that help to address issues debated in the literature and also suggest pathways for future research.

Day 2 - Wednesday

The role of equation residuals in the discovery of anomalous PDE solutions

Eloisa Bentivegna, IBM
Wednesday, 09:40-10:00, Room 2

Nonlinearities are pervasive in Physics, leading to complex phase portraits and a correspondingly rich phenomenology in many domains. For continuum systems, nonlinear Partial Differential Equations (PDEs) are typically used to model the system’s behaviour. Exploring a nonlinear PDE’s solution space in search for any equilibria, transitions between phases, and other critical phenomena is a complex undertaking, as interactions between a system’s degrees of freedom lead to novel branches which have no counterpart in the linear regime. This may result in the emergence of anomalous or extreme solutions; identifying all of them via brute force is an intractable problem. I will discuss an approach to extreme-solution discovery based on the study of the structure of the PDE residual and its relationship to solution variability. This approach allows to classify the solution space solely based on the structure of the governing equation, thus avoiding the need for expensive numerics. I will illustrate this framework with a few examples. Finally, I will describe how this information could be used in a Physics-Informed—AI setting to build emulators that can capture these solutions accurately.

Estimating Quasipotentials and Minimum Action Paths of a three-box model of the Atlantic Meridional Overturning Circulation using an Ordered Line Integral Method

Ruth Chapman, University of Copenhagen
with Peter Ashwin, University of Exeter
Wednesday, 09:40-10:00, Room 1

Tipping phenomena is an active area of research, especially in Earth systems which display bi-stability. The Atlantic Meridional Overturning Circulation (AMOC) is considered a core tipping element, and many models of varying complexity have shown it to display bi- and multi-stability. Here, we use an Ordered Line Integral Method (OLIM) to estimate the quasipotential of a process-based box model of the AMOC, using the method of Dahiya and Cameron (2018). Calculating the quasipotential allows us to further understand the dynamical properties of this three-box model, and calculate a minimum action paths (MAPs) between stable states. We calculate MAPs for isotropic, anisotropic and exaggerated noise structures. The anisotropic noise used is estimated from CMIP6 pre-industrial control experiments, and expected to better model real-world ocean variability than isotropic noise. We find in cases of higher noise, that saddle-avoidance is possible, however, our anisotropic noise structure does not display this behaviour. Finally, we use these results to consider a physical early-warning signal for this system.

Data-driven approach for modelling complex systems using a multivariate non-parametric Langevin equation

Antonio Malpica-Morales, Imperial College London
with Miguel A. Duran-Olivencia, Imperial College London; Serafim Kalliadasis, Imperial College London
Wednesday, 10:00-10:20, Room 2

We introduce a data-driven methodology to approximate the stochastic behaviour of real-world complex systems. The foundation of our framework consists of a multivariate Langevin equation with flexible drift and diffusion terms, eliminating the need for prior understanding of the system being analysed. Such flexibility relies on the relationship between the drift-diffusion terms and the Kramers-Moyal coefficients. By estimating the Kramers-Moyal coefficients through a kernel density approach, a non-parametric technique, we ensure a high level of adaptability and intricate functional representation. We exemplify our framework's effectiveness using a classical particle in a bistable potential, highlighting the reconstruction of a simple metastability effect. Additionally, we successfully illustrate our framework's dependability with two examples from financial markets: the Spanish electricity day-ahead prices and the EURUSD and GBPUSD currency-exchange rates. While univariate models, such as the Ornstein-Uhlenbeck process and the geometric Brownian motion, dominate standard practice in these fields, our non-parametric multivariate Langevin equation represents a novel approach. Its multivariate capability extracts different equilibrium points and diffusion behaviours of the system that remain elusive in univariate settings.

Quasi-potential landscape in a bistable cloud system

Benjamin Hernandez, TU Delft
with Franziska Glassmeier, TU Delft
Wednesday, 10:00-10:20, Room 1

Clouds are an integral part of our climate system, as they play a fundamental role in the Earth’s energy budget and water cycle. Among these, stratocumulus cloud decks stand out as the largest cloud type by coverage, characterized by their distinctive bistable cellular patterns. Despite their significance, current climate models struggle to accurately represent these clouds, leading to considerable uncertainties in our climate projections. In this study, we employ a two-dimensional dynamical system framework to investigate stratocumulus cloud fields. The system is characterized by a double saddle-node bifurcation in all major parameters, showing two attractors with substantially different relaxation times. We model transitions between cloud states as noise-driven processes and analyze the effects of large fluctuations on the system. Using large-deviation theory, we map out the global Freidlin-Wentzell quasi-potential landscape and compute the instanton paths between the two cellular states. We demonstrate how anti-correlated fluctuations between the two state variables significantly facilitate these transitions. Furthermore, we study how the stability of the attractors changes under different future climate scenarios and propose modeling rare, strong fluctuations (such as the effects of ship tracks) using Lévy noise.

Siegmund Duality in Physics: a bridge between spatial and first-passage properties of stochastic processes

Léo Touzo, ENS Paris
with Mathis Guéneau, Sorbonne Université
Wednesday, 11:00-11:20, Room 1

First-passage problems are relevant in many different contexts, ranging from chemistry and biology to mathematical finance. Considering a stochastic particle in 1d, evolving on an interval [a,b], with absorbing walls at a and b, the goal is to answer questions such as: What is the probability that it reaches b before reaching a ? What is the distribution of the exit time ? These questions happen to be related to a completely different type of problem, namely the computation of the spatial distribution of a stochastic particle with hard walls at a and b. This is known in the mathematical literature as Siegmund duality. It was first observed for Brownian motion, but it has since then been extended to a variety of stochastic processes. However, this connection remains relatively unknown among physicists. I will show how this property can be extended to a variety of non-Markovian processes which are of particular interest in physics. I will focus on a particular class of models, for which both first-passage problems and interactions with hard walls are especially relevant: active particles, models of self-propelled particles inspired from the motion of living organisms such as bacteria. Based on: M. Guéneau, L. Touzo, 2024 J. Phys. A: Math. Theor. 57 225005, and M. Guéneau, L. Touzo, 2024 arXiv:2404.10537.

Applying complex networks to climate simulations with global-scale tipping

Laure Moinat, University of Geneva
with Jérôme Kasparian, University of Geneva // Maura Brunetti, University of Geneva
Wednesday, 11:00-11:20, Room 2

Early Warning Signals (EWS) are indicators that can be used to prevent abrupt changes in the climate system, and are especially relevant for quantifying the risk of crossing tipping points in the present-day climate change. Classically, EWS are investigated using statistics on time series of climate state variables, without considering their spatial distribution. However, spatial information is crucial to identify the starting location of a transition process and can be directly inferred by satellite observations. We use surface air temperature on a numerical grid as a complex network and seek for network properties that can be used as EWS when approaching the state transition. We show that the network indicators are able to detect tipping points at the global scale, as simulated in a coupled-aquaplanet configuration with the MIT general circulation model using as forcing parameter the atmospheric CO$_2$ content. The application of such indicators as EWS is evaluated and compared to the classical ones.

Data-driven anticipation and prediction of Atlantic Meridional Overturning Circulation collapse using non-autonomous spatio-temporal dynamical modelling

Frank Kwasniok, University of Exeter
Wednesday, 11:20-11:40, Room 2

A data-driven methodology for identifying, anticipating and predicting critical transitions in high-dimensional model or observational data sets is introduced, based on explicit non-stationary low-order modelling of the tipping dynamics, allowing for dynamical understanding of the underlying tipping mechanism and genuine prediction of the future system state by extrapolation. A set of spatial modes carrying the tipping dynamics are identified and a stochastic model of appropriate complexity is estimated in the subspace spanned by these modes. Analysis of the reconstructed dynamics allows to determine the proximity to a bifurcation point and the type of the impending bifurcation. Different competing tipping mechanisms can be compared and assessed using likelihood inference and information criteria. The method allows to quantify the likelihood or risk of a critical transition at some point in the future having observed a certain amount of data up to present. The methodology is here applied to a data set from a simulation of AMOC collapse with a complex climate model, actually a freshwater hosing experiment with the FAMOUS GCM. The AMOC on-state is found to lose stability via a subcritical Hopf bifurcation; however, the transition to the off-state occurs far ahead of the bifurcation point. The early collapse can be explained by a combination of rate-induced and noise-induced tipping.

Transition path sampling for SDEs

Raphael Römer, University of Exeter
with Tobias Grafke, Reyk Börner, Ryan Deeley
Wednesday, 11:20-11:40, Room 1

Sampling statistical properties of noise induced transition paths via rejection sampling is numerically expensive for weak noise as transitions are only rarely observed. However, for gradient stochastic differential equations (SDEs) with additive noise, it was shown by Hairer Stuart and Voss that a corresponding stochastic partial differential equation (SPDE) allows an efficient way of sampling the SDE’s transition paths. We explore how this method can be used in the case of degenerate noise and in systems with non-gradient drift. Further, we show how the transformation of the SDE into the corresponding SPDE gives rise to an intuitive understanding of the non-gradient phenomenon of “saddle avoidance” where transition paths between competing attractors can cross the basin boundary far away from the saddle in between.

The Rise and Fall of Carbon Cycle Instabilities

Perrin W. Davidson, Massachusetts Institute of Technology
with Daniel H. Rothman, Massachusetts Institute of Technology
Wednesday, 14:00-14:20, Room 2

Observational records of the global carbon cycle show apparent instabilities throughout the last 66 Myr of the Cenozoic. The question we aim to address is deceptively simple: how do these instabilities come into and out of existence? Recent work has demonstrated that we can treat the carbon cycle as a nonlinear, non-autonomous dynamical system – that is, one that displays characteristic behavior through time, driven by time-dependent forcings. Coupling observation with theory, we hypothesize that such instabilities are excitations from a stable state to which the carbon cycle eventually relaxes. Given timing uncertainties, we develop an algorithm to extract characteristic carbon cycle excitations in a Cenozoic climate proxy record. Analysis identifies pre-onset excursions and successor asymmetries. Informed by these results, we formulate a low-dimensional, damped model of the global carbon cycle that exhibits excitations both qualitatively and quantitatively similar to Cenozoic data.

Tipping in magnetohydrodynamic channel flow through continuation of edge states

Mattias Brynjell-Rahkola, DAMTP, University of Cambridge
with Yohann Duguet, LISN-CNRS, Université Paris-Saclay; Thomas Boeck, Institut für Thermo- und Fluiddynamik, Technische Universität Ilmenau
Wednesday, 14:00-14:20, Room 1

In fluid systems, subcritical transition to turbulence is possible when the laminar and the turbulent states are in competition as attractors. There are many situations in which the flow is subject to a volume force such as the Coriolis, buoyancy or Lorentz force that are known to have a damping effect on fluctuations. Under these circumstances, subcritical transition may be envisioned with respect to the strength of the forcing. Here we investigate this scenario for the magnetohydrodynamic channel flow, in which the strength of the Lorentz force is characterized by the Hartmann number. Specifically, the turbulent state is shown to become metastable for a fixed Reynolds and a sufficiently large Hartmann number, which complicates the determination of the tipping point. As an alternative, the study of edge states that reside on the laminar-turbulent basin of attraction is proposed. In the talk, results from large-scale direct numerical simulations that reveal the change in edge state dynamics with Hartmann number are presented. Although traditional early warning signals fail to predict the tipping, it is illustrated how the continuation of edge states enables accurate determination of the bifurcation.

Mapping and control of high-dimensional, delay-induced bistability from noisy data

Kevin Daley, United States Naval Research Laboratory
with Jason M. Hindes, United States Naval Research Laboratory Ira B. Schwartz, United States Naval Research Laboratory
Wednesday, 14:20-14:40, Room 1

Multistability in high-dimensional complex systems such as partial differential equations and large multi-agent swarms poses a unique challenge to modeling and control in experiments. Frequently, such systems' state spaces contain significant regions of dynamical uncertainty where, in the presence of small-amplitude observation noise, robust control schemes and avoidance of undesirable dynamical regimes are intractable. We consider an example high-dimensional dynamical system with bistability and an embedded saddle and introduce a novel, equation-free procedure for determining the location of the saddle in the state space of the system by projection of the dynamics onto a smooth neural network approximation of its stable manifold trained on a noisy set of sample points. Notably, our approach assumes only the ability to generate a dense sample of trajectories and classify their asymptotic behavior, allows for precise control of complex systems even close to uncertainty, and yields an accurate estimate of the minimum embedding dimension of the stable manifold of the saddle which determines the reducibility of the corresponding control problem. We discuss applications of this method to complex engineering systems such as multi-agent swarms.

Predictability of tipping in a climate model featuring a multistable ocean circulation

Johannes Lohmann, University of Copenhagen
Wednesday, 14:20-14:40, Room 2

We study the dynamics of a global ocean model, featuring a complex multistability of the Atlantic circulation, under different time-varying forcings. Transitions from a state of vigorous, present-day Atlantic Meridional Overturning Circulation to a state of collapsed circulation are induced by the influence of climate change or stochastic perturbations. The predictability of transitions, and thus of the future climate state, can be limited, due to chaotic dynamics and non-autonomous dynamical effects. The simulations are used to argue for two points that we believe are more generally applicable for multistable, non-autonomous complex systems: a) Due to partial tipping (a splitting of an ensemble of initial conditions under time-varying forcing) in a chaotic system, there is a loss of predictability of the future attractor. But for systems that are stationary in the past limit, a new type of predictability arises, by which the probabilities of tipping to different future states can be calculated using ensemble simulations with arbitrary initial conditions. b) When the system is subjected to stochastic forcing and a monotonic parameter shift, an impending crisis may be better predicted by early-warning signals that are designed from knowledge of the transition instanton and/or an edge state.

Most Likely AMOC Collapse in a Stochastic Boussinesq Fluid Model

Jelle Soons, Utrecht University
with Tobias Grafke, University of Warwick; Henk A. Dijkstra, Utrecht University
Wednesday, 14:40-15:00, Room 2

The present-day Atlantic Meridional Overturning Circulation (AMOC) is a core tipping element and its collapse would have grave consequences on the global climate. Therefore, it is important to determine probabilities and pathways for noise-induced tipping events. However, as there is no observational evidence for an AMOC transition over the historical period, a noise-induced transition is expected to be a rare event in models and simple Monte Carlo techniques are unsuited for such low-probability events. Here, we use the Freidlin-Wentzell Theory of Large Deviations to directly compute the most probable transition pathways for a collapse of the AMOC in a two-dimensional spatial model of a surface-forced Boussinesq flow with stochastic freshwater forcing. Now we can determine the physical mechanisms of the collapse of the AMOC. Surprisingly, it initially starts with a strengthening of the overturning cell followed by the occurrence of a second overturning cell in the southern end of the basin. This is achieved by a large salinity impulse onto the southern surface area. The separatrix is reached when the system has two symmetric overturning cells with asymmetric heat and salinity distribution. Due to the restoring temperature forcing eventually the unstable symmetric saddle state is reached from whereon the original northern overturning cell collapses. An energy analysis of the trajectory shows that the main driver behind the collapse is the net cooling done at the surface which is only partially countered by diffusive mixing. Moreover, this method also allows us to estimate the ratios of probabilities to collapse between scenarios with varying distances to the bifurcation tipping point, showing that this probability sharply increases when approaching this point.

Using Witten Laplacians to locate index-1 saddle points

Panos Parpas, Imperial College London
with Tony Lelièvre, Ecole des Ponts
Wednesday, 14:40-15:00, Room 1

We introduce a new stochastic algorithm to locate the index-1 saddle points of a function $V:\R^d \to \R$, with $d$ possibly large. This algorithm can be seen as an equivalent of the stochastic gradient descent which is a natural stochastic process to locate local minima. It relies on two ingredients: (i) the concentration properties on index-1 saddle points of the first eigenmodes of the Witten Laplacian (associated with $V$) on $1$-forms and (ii) a probabilistic representation of a partial differential equation involving this differential operator. Numerical examples on simple molecular systems illustrate the efficacy of the proposed approach.

Uncertainty quantification for overshoots of tipping thresholds

Paul Ritchie, University of Exeter
with Kerstin Lux-Gottschalk, Eindhoven University of Technology
Wednesday, 15:00-15:20, Room 2

Many subsystems of the Earth are at risk of undergoing abrupt transitions from their current stable state to a drastically different, and often less desired, state due to anthropogenic climate change. One common mechanism for tipping to occur is via forcing a nonlinear system beyond a critical threshold that signifies self-amplifying feedbacks inducing tipping. However, previous work has shown that it is possible to briefly overshoot a critical threshold and avoid tipping. For some cases, the peak overshoot distance and the time a system can spend beyond a threshold are governed by an inverse square law relationship. In the real world or complex models, critical thresholds and other system features are highly uncertain. In this presentation, we look at how such uncertainties affect the probability of tipping from the perspective of uncertainty quantification. We show the importance of constraining uncertainty in the location of the critical threshold and the linear restoring rate to the system’s stable state in a simple box model for the Atlantic Meridional Overturning Circulation (AMOC). Thereby, we highlight the need to constrain the highly uncertain diffusive timescale within the box model to reduce tipping uncertainty for overshoot scenarios of the AMOC.

Efficacy and reliability of early warnings to critical transitions in a non-autonomous turbulent reactive flow system

Ankan Banerjee, Department of Applied Mathematics, University of Leeds, UK
Wednesday, 15:00-15:20, Room 1

The quest for early warning signals (EWSs) flagging transitions to unwanted states in real-world complex systems, remains an outstanding problem. The situation is more intricate in the the presence of time-dependent forcing and inherent fluctuations present in the system. This talk is about our understanding of the efficacy of different EWSs and their robustness in providing true alarms in the context of a non-autonomous turbulent thermoacoustic system prone to thermoacoustic instability (TAI). The phenomenon of TAI has catastrophic consequences as it could lead thermoacoustic systems to break down. A few examples of thermoacoustic systems are gas turbine engines used for power production, and liquid rocket engines or jet engines used for aviation. Such turbulent systems possess inherent fluctuations. We analyse EWSs obtained from critical slowing down, and spectral and fractal characteristics of the system. According to our analysis fractal and spectral-based EWSs are more robust and reliable in providing true warnings to TAI, at different rates of forcing. The talk will also highlight the role of neural operators such as Fourier neural operators in reproducing zonal jets and predicting extreme climate events with a hope to resolve open problems associated with metastability.

Day 3 - Thursday

Response Theory Identifies Reaction Coordinates and Explains Critical Phenomena in Noisy Interacting Systems

Valerio Lucarini, University of Leicester
with Niccolo' Zagli, NORDITA and Greg Pavliotis, Imperial College London
Thursday, 09:40-10:00, Room 1

We consider a class of nonequilibrium systems of interacting agents with pairwise interactions and quenched disorder in the dynamics featuring, in the thermodynamic limit, phase transitions. We provide conditions on the microscopic structure of interactions among the agents that lead to a dimension reduction of the system in terms of a finite number of reaction coordinates. Such reaction coordinates prove to be proper nonequilibrium thermodynamic variables as they carry information on correlation, memory and resilience properties of the system. Phase transitions can be identified and quantitatively characterised as singularities of the complex valued susceptibility functions associated to the reaction coordinates. We provide analytical and numerical evidence of how the singularities affect the physical properties of finite size systems. Ref.: arXiv:2303.09047

Chimera-inspired dynamics: When higher-order interactions are expressed differently

Xinrui Ji, Institute of Complex Networks and Intelligent Systems, Shanghai Research Institute for Intelligent Autonomous Systems, Tongji University, Shanghai 201210, China
with Xiang Li, Institute of Complex Networks and Intelligent Systems, Shanghai Research Institute for Intelligent Autonomous Systems, Tongji University, Shanghai 201210, China
Thursday, 09:40-10:00, Room 2

The exploration of chimera-inspired dynamics in nonlocally coupled networks of Kuramoto oscillators with higher-order interactions is in its early stages. Concurrently, the investigation of collective phenomena in higher-order interaction networks is gaining traction. Our study reveals that hypergraphs tend to synchronize through lower-order interactions, whereas simplicial complexes exhibit a preference for higher-order interactions. This distinction suggests substantial differences in chimera-inspired synchronization regions for higher-order representations. We introduce an explicit expression for identifying the chimera state, supported by a comprehensive basin stability analysis. By examining the interplay of pairwise and higher-order interaction strengths, we demonstrate that the emergence of chimera states is inherent in high-order interaction networks. This behavior is indicative of tipping points in the system, where small changes in interaction strengths or initial conditions can lead to abrupt transitions. Our findings advance the understanding of chimera-inspired dynamics in higher-order interaction networks, paving the way for deeper insights into their intricate dynamics.

Constructing Response Operators Using Koopman Formalism

John Moroney, University of Leicester
with Valerio Lucarini
Thursday, 10:00-10:20, Room 1

Linear response theory may be used to predict the existence of tipping points in complex systems. High sensitivity to perturbations and the slow decay of response functions is associated with critical transitions. However, traditional methods of constructing response operators lack the property of interpretability. We present a method of constructing response operators that are expressed in terms of the natural modes of variability of the system. In the context of climate, this may provide a means of determining the impact of anthropogenic forcing on known of modes of climate variability. We do this by taking advantage of a Koopman operator approach to represent the chaotic dynamics of a system in terms of the eigenvalues and eigenfunctions of an infinite-dimensional linear operator. Using data-driven methods, it is then possible to obtain a finite-dimensional representation of this operator. We demonstrate in a few low-dimensional models how correlation functions of observables, and thus response functions may be represented by a sum of Koopman eigenfunctions, with time dependence determined by the eigenvalues, which are independent of the forcing applied.

Scaling laws in turbulent thermal convection

Camilla Nobili, University of Surrey
Thursday, 10:00-10:20, Room 2

Scaling laws are a useful tool in studying and characterizing geophysical flows as they may indicate their behaviour in extreme parameter regimes which are unapproachable by experiments. In particular, the challenge of finding scaling laws requires synergetic efforts involving laboratory, computational, and theoretical studies. In fact, deducing and calibrating scaling laws requires physical arguments, analytical bounding methods, numerical analysis and experiments. We will focus on convection problems as they are a relevant in a multitude of natural phenomena in meteorology, oceanography and industrial applications. In this talk we will present the latest rigorous results concerning bounds for the heat transport enhancement in turbulent regimes.

Tipping phenomena in inertial focusing of particles

Rahil Valani, University of Oxford
with Brendan Harding, Victoria University of Wellington; Yvonne Stokes, University of Adelaide
Thursday, 11:00-11:20, Room 1

Small finite-size particles suspended in fluid flow through an enclosed curved duct can focus to attractors (such as fixed points or limit cycles) in the two-dimensional duct cross-section. This particle focusing is a result of a balance between two dominant forces acting on the particle: (i) the inertial lift force arising from small but non-negligible inertia of the fluid, and (ii) the secondary drag force due to the cross-sectional vortices induced by the curvature of the duct.This phenomenon has been exploited in various industrial and medical applications to passively separate particles by size using purely hydrodynamic effects. I will present results of our numerical exploration of particle dynamics in spiral duct geometries with slowly varying curvature. We observe rich nonlinear particle dynamics and various types of tipping phenomena, such as bifurcation-induced tipping (B-tipping), rate-induced tipping (R-tipping) and a combination of both. I will discuss implications of these unsteady dynamical behaviours for separating particles by size.

The Challenge of Non-Markovian Energy Balance Models in Climate

Nicholas Wynn Watkins, Grantham Research Institute on Climate Change & the Environment, LSE
with Raphael Calel, Georgetown University, USA; Sandra Chapman, University of Warwick, UK; Aleksei Chechkin, Akhiezer Institute for Theoretical Physics, Ukraine; Rainer Klages, QMUL, UK; David Stainforth, LSE, UK.
Thursday, 11:00-11:20, Room 2

Hasselmann’s stochastic paradigm of 1976 works on several levels. One is a way to add natural variability into Budyko-Sellers energy balance models (EBMs). At a more abstract level it used the origianl model of Brownian motion to provide a link between slow climate variability and fast weather fluctuations, leading him to posit a need for negative feedback in climate models. The resulting stochastic EBM maps onto the simplest linear Markovian stochastic process. This presentation highlights two newer developments of Hasselmann’s pioneering ideas. One important one has been the use of the Mori-Zwanzig method to embeds EBMs in the more comprehensive Generalised Langevin Equation (GLE) framework, reviewed for climate applications by Lucarini and Chekroun (2023). Another has been the evidence, acknowledged by the Nobel committee, for “long range” memory with a slower decay than the exponential form assumed by Hasselmann. This presentation, based on Watkins et al (Chaos, to appear, 2024) will argue that the Mori-Kubo stochastic GLE, widely used in statistical mechanics suggests a relatively simple but nonetheless non-Markovian stochastic EBM for the global temperature anomaly. It generalises Lovejoy et al’s Fractional Energy Balance Equation, allowing more flexibility in the choice of memory, not just a power law.

A non-autonomous framework for climate change and extreme weather events increase in a stochastic energy balance model

Gianmarco Del Sarto, Scuola Normale Superiore
with Franco Flandoli, Scuola Normale Superiore
Thursday, 11:20-11:40, Room 2

We develop a three-timescale framework for modelling climate change and introduce a space-heterogeneous one-dimensional energy balance model. This model, addressing temperature fluctuations from rising carbon dioxide levels and the super-greenhouse effect in tropical regions, fits within the setting of stochastic reaction-diffusion equations. Our results show how both mean and variance of temperature increase, without the system going through a bifurcation point. This study aims to advance the conceptual understanding of the extreme weather events frequency increase due to climate change.

Dual-tipping in multiscale systems: noise introduces uncertainty to rate-dependent transition scenarios

Ryan Deeley, Carl von Ossietzky Universität Oldenburg
with Peter Ashwin, University of Exeter, Ulrike Feudel, Carl von Ossietzky Universität Oldenburg
Thursday, 11:20-11:40, Room 1

Sudden, drastic shifts in a dynamical system’s variables describe critical transitions when they represent high-impact, long-lasting global changes. Critical transitions are paramount to climate science, and great advances have come in modelling their onset using nonautonomous systems. In particular, critical thresholds can be reached when varying an external input faster than the system’s response rate (R-tipping), or following a harmful accumulative series of stochastic perturbations (N-tipping). Often studies prescribe one and only one of these mechanisms for environmental models, yet in reality, they act in conjunction and their effects cannot be fully decoupled. We present - within i) paradigmatic and ii) multiscale systems - how noise introduces uncertainty to rate-dependent transition scenarios. We analyse ensembles of coupled noise- and rate-driven trajectories that transition to alternative states for rates below the critical threshold associated with R-tipping; conversely, we study cases where noise prevents a system from undertaking the rate-induced transition that would occur without noise. By constructing a delayed committor function, we assess the probability that a rate-dependent tracking/tipping scenario changes under the influence of noise. Further, we compute most probable coupled noise- and rate-induced tracking/tipping paths by solving associated Euler-Lagrange equations, and compare their solutions to ensembles of numerical simulations.

Posters

Towards Understanding Trap Counts Obtained by a Baited Trap: A Simulation-based Study

Omar Alqubori, University of Jeddah
with Sergei Petrovskii and Daniel Bearup, University of Leicester

In insect ecology, it is important to understand insect's movement and behaviour. However, insects change their movement when their behaviours are changed. We could use traps to understand how the insect's behaviours change. The most common traps that affect the insect's behaviour is a baited trap because the movement pattern changes from Correlate Random Walk to Bias Random Walk (BRWs). This, in turn, shows how the insect's behaviour changes. In this paper, we suppose the insect's behaviour changes in the step size and turning angle. That is four different behaviours in turning angle and five in step size.

Transfer operator approach to stability analysis of stochastic glacial-interglacial model.

Jakob Harteg, Potsdam Institute for Climate Impact Research
with Nico Wunderling (Center for Critical Computation Studies, Frankfurt), Jonathan F. Donges (Potsdam Institute for Climate Impact Research)

In this study, we employ a reduced-complexity ice age model by Talento & Ganopolski (2021), extended with stochastic additive noise, to produce an ensemble of alternative global mean ice volume trajectories over the last 800,000 years. The spread of the stochastic trajectories varies greatly throughout the simulation, allowing for the identification of roughly three regimes: 1) all trajectories approximately follow the same path, 2) trajectories gradually spread out, and 3) only a few possible paths are accessible. We attempt to apply the spectral gap of the transfer operator, computed using Ulam’s method in a sliding time window, as an indicator of global stability, hoping that a large spectral gap would identify periods of stability where all trajectories roughly follow the same path. In reality, it turns out to be more complicated, and a meaningful approach is yet to be discovered. Challenges include the model being nonautonomous (due to orbital forcing) and non-Markovian (due to an ice-volume integrating memory term), which breaks the semi-group property of the transfer operator, preventing a reliable approximation of the spectral gap, as well as selecting appropriate values for the transition time lag and length of the sliding window.

Assessment of Abrupt Shifts in CMIP6 Models using Edge Detection

Sjoerd Terpstra, Utrecht University
with Swinda K.J. Falkena, Utrecht University; Robbin Bastiaansen, Utrecht University; Sebastian Bathiany, Technical University of Munich; Henk A. Dijkstra, Utrecht University; Anna von der Heydt, Utrecht University

Many potential tipping elements in the climate system have been identified over the past decade, but there are large uncertainties regarding their timing and spatial extent. Some tipping points might express themselves as abrupt shifts, with potentially drastic consequences on the climate system, dependent ecosystems, and society. This study presents an updated analysis of the likelihood of these abrupt shifts in the latest generation of climate models (CMIP6). We analyze 59 CMIP6 models under a scenario of a yearly 1% increase in CO2, using a Canny edge detection method - adapted for spatiotemporal dimensions - to detect abrupt shifts occurring on time scales from years to decades. Our semi-automatic analysis covers 83 variables across the ocean, atmosphere, and land. Using connected component analysis, we quantify the spatial extent of abrupt shifts. We focus our analysis on the following systems: North Atlantic subpolar gyre, Tibetan plateau, land permafrost, Amazon rainforest, Antarctic Sea Ice, monsoon systems, Arctic Summer Sea Ice, Arctic Winter Sea Ice, and Barents Sea Ice. For these systems, we study the number of detected abrupt shifts, their surface area, and at which global mean temperature they occur. We find evidence of abrupt shifts in most systems, but not all models show them equally.

A variational approach to explore transitional behaviour in solutions of the Sachs equation governing the propagation of light in space-time

Jonathan Wong, IBM Research Europe

The cosmological model of the Universe, and the corresponding spacetime metric that characterises the gravitational field, are of fundamental significance to theoretical physics and astronomy. This framework represents a complex physical system in which particular unique solutions can either give rise to extreme observational phenomena, such as Einstein rings of galaxies, or could indicate a critical instability point in the underlying theory, such as the singularity of a black hole. In order to investigate such distinct properties of the gravitational field one can explore the optical scalars, a set of functions that measure the expansion, shear and rotational twist of a test circle as it propagates along a light path. This behaviour is characterised by the Sachs equations (Sachs 1961), a set of coupled differential equations in each scalar quantity that describe their overall evolution. In this study we explore and search for extreme transitional behaviour in solutions of the optical scalar equations that arise from a range of underlying cosmological models. We investigate in particular anisotropic Bianchi Type I cosmologies, and predict the effect that such extreme solutions will place on astrophysical signals, such as the (weak) gravitational lensing of galaxies by the large scale structure of the Universe.

Using a variational framework to detect transitions between invasion and extinction in a mathematical model of collective migration

Joseph Pollacco, IBM Research Europe
with Eloisa Bentivegna, IBM Research Europe

In collective migration problems, such as establishment of invasive species and disease spread, an understanding whether an invasion can and will be successful is vitally important. Realistic models of spatial invasion, typically formulated as partial differential equations with travelling wave solutions, thus often encompass transitions between successful invasion and extinction. Such transitions are usually under different parameter regimes which are not known a priori. In this work, we seek to demonstrate that these transitions can be detected using a variational approach. Using a reaction-diffusion equation with Allee (cubic) reaction kinetics and simple diffusion as a prototype model of collective invasion in one dimension, we detect a parameter-induced transition between solutions describing invasion and extinction. We further apply the variational approach to extensions of this reaction-diffusion equation with variable diffusion coefficient, and in two dimensions to characterise the conditions under which the solution behaviour changes in this framework. We link these conditions to previous characterisations. Overall, our work links traditional analysis of reaction-diffusion equations with a new approach for detecting parameter-induced transitions in solution behaviour.

An approach to find markers of dynamical transitions in metastable epileptic seizure state systems

Callum Matthew Simpson, IBM research Europe
with Eloisa Bentivegna, IBM research Europe

Epilepsy is a neurological disorder characterised by frequent seizures which can be depicted as metastable excited states. Epileptic spike-wave seizures are pronounced as abnormal cadence discharging of electrical activity within the brain. This cadence is an indication of underlying deterministic nonlinear oscillation. The early termination of spike-wave seizures can be achieved through single-pulse stimulus perturbations; however, this is not always successful. The dynamic transition between the background activity and epileptic seizure states is not fully understood. Questioning the system exhaustively can be difficult as it’s influenced by several factors. Recent work has shown that the markers of dynamical transitions in nonlinear dynamical systems can be explored through the functional derivatives of the equation residual. Using a neural population model to represent the epileptic spike waves within the thalamo-cortical coupling we structure the background activity basin of attraction as a four-dimensional object. We aim to find markers of dynamical transitions that solely depend on the form of the governing equation. Results from this work can lead to a better understanding of the success rate of stimuli responses to patient specific seizures simulations, further translating to the administration of high success rate stimulus to moderate real seizures.

Tipping points in the parameter space of blow-up solutions in 3D fluid models

Navonil Neogi, IBM Research Europe

Fluid equations constitute prototypical examples of complex systems. Simple models of fluids exhibit tipping points between regimes of smooth solutions and ‘blow-ups’, or singularities, within finite time. Establishing the existence of these and constructing examples is fundamental to the field. Recent work has established such ‘blow-up’ solutions robustly for the first time in the case of the 3D Euler equation—a well-studied nonlinear PDE that models inviscid flow—with a cylindrical boundary. These solutions are self-similar, preserving an initial spatial profile propagated through time, and were found using an AI surrogate in the form of a physics-informed neural network (PINN) encoding the symmetries of the problem. Our research aims to explore this dynamical system using a variational approach, on the parameter space of self-similar solutions (controlled by an exponent). We aim to detect transitions in this approach between blow-up and non-blow-up solutions from the exponent parameter. We also aim to apply this approach to further fluid models, also studied using PINN solvers, that are known to exhibit blow-up behaviour. The results would be important for greater theoretical understanding of how and where blow-ups occur, and their sensitivity to parameters.

Conditions for Instability in the Climate-Carbon System

Joseph Clarke, University of Exeter
with Paul Ritchie, University of Exeter; Chris Huntingford, UK Centre for Ecology and Hydrology; Mark Williamson, University of Exeter; Peter Cox, University of Exeter

The CMIP6 project revealed that some of the latest generation of climate models show a very strong response to increased concentrations of atmospheric CO2, as quantified by equilibrium climate sensitivity (ECS). This high sensitivity has implications for the carbon cycle. For example, at higher climate sensitivities, a small CO2 perturbation leads to larger warming, which in turn causes increased decomposition of organic matter. This increased decomposition tends to increase atmospheric CO2, leading to a positive feedback loop. Over the last 10,000 years or so (the Holocene epoch), atmospheric CO2 concentrations have remained approximately constant, at least until the anthropogenic perturbation from the industrial revolution. This means that the feedback loop cannot be too strong, placing bounds on equilibrium climate sensitivity. CMIP6 climate models, however, cut this feedback loop out by running with prescribed levels of CO2. We investigate using models of varying complexity, performing a bifurcation analysis to determine the climate sensitivies incompatible with the stable Holocene carbon cycle.

Symbolic regression for unveiling hidden mechanisms behind tipping points

Eva van Tegelen, Wageningen University
with Ioannis Athanasiadis, Peter van Heijster, George van Voorn (Wageningen University)

Although machine learning methods have demonstrated their ability to capture dynamics from time series data, the prediction of sudden transitions, such as tipping points, remains a significant challenge. Since tipping of large-scale systems could onset impacting changes and presents a significant risk for human welfare, understanding the mechanisms behind tipping points is essential. In our research we use machine learning methods to obtain mathematical model descriptions from data, also known as symbolic regression. These equations would allow exploration of a wide range of possible outcomes and could aid in anticipating and possibly preventing sudden shifts or even collapse in a system. Although in recent years different symbolic regression algorithms have been successful in obtaining accurate model descriptions, it has not been applied as a tool to understand systems exhibiting tipping behaviour. Our research aims at developing symbolic regression algorithms such that they can be applied to systems undergoing bifurcations due to changing environmental parameters and external forces.

Generating long time scales by tuning to criticality in actin condensates

Tal Agranov, University of Cambridge

How does a biological system manage to produce long time scales that vastly outlast intrinsic biochemical rates, yet are not infinite? This challenge features in various biological tasks involving memory and sensing. In this work, we uncover how this manifests in the cellular assembly of a C. elegans embryo. High-resolution imaging reveals that the cell’s actin cortex formation is preceded by a stage where thousands of highly branched actin structures transiently grow and disassemble. Some structures grow orders of magnitude past their intrinsic degradation time, yet without proliferating. We uncover how an overlooked bifurcation in the underlying biochemical dynamics can account for the huge lifetime disparity. We show how a simple mechanism based on resource competition can explain how this process spontaneously self-tunes to the vicinity of this dynamical bifurcation.