Related papers: A mathematical framework for critical transitions:…

There have been significant recent advances in our understanding of the potential use and limitations of early-warning signs for predicting drastic changes, so called critical transitions or tipping points, in dynamical systems. A focus of…

In several natural and engineering systems, changes in control parameters can trigger bifurcations that lead to sustained or growing periodic oscillations, indicating the onset of oscillatory instabilities. Such emergent behaviour often…

Nonlinear dynamical systems subjected to a combination of noise and time-varying forcing can exhibit sudden changes, critical transitions or tipping points where large or rapid dynamic effects arise from changes in a parameter that are…

Many dynamical systems, including power systems, recover from perturbations more slowly as they approach critical transitions---a phenomenon known as critical slowing down. If the system is stochastically forced, autocorrelation and…

Catastrophic transitions, where a system shifts abruptly between alternate steady states, are a generic feature of many nonlinear systems. Recently these regime shift were suggested as the mechanism underlies many ecological catastrophes,…

Recent work has highlighted the utility of methods for early warning signal detection in dynamic systems approaching critical tipping thresholds. Often these tipping points resemble local bifurcations, whose low dimensional dynamics can…

We study the maximum mean discrepancy (MMD) in the context of critical transitions modelled by fast-slow stochastic dynamical systems. We establish a new link between the dynamical theory of critical transitions with the statistical aspects…

A generic saddle-node bifurcation is proposed to modelize fast transitions of finite amplitude arising in geophysical (and perhaps other) contexts, when they result from the intrinsic dynamics of the system. The fast transition is…

Noise plays a fundamental role in a wide variety of physical and biological dynamical systems. It can arise from an external forcing or due to random dynamics internal to the system. It is well established that even weak noise can result in…

The early prediction of tipping points, distinguished by sudden and catastrophic shifts from stable states, poses a challenging task that would enable us to assess the impending threat across natural and engineered systems. This threat…

Anticipating bifurcation-induced transitions in dynamical systems has gained relevance in various fields of the natural, social, and economic sciences. Before the annihilation of a system's equilibrium point by means of a bifurcation, the…

We consider a model for substrate-depletion oscillations in genetic systems, based on a stochastic differential equation with a slowly evolving external signal. We show the existence of critical transitions in the system. We apply two…

Nonlinear dynamical systems exposed to changing forcing can exhibit catastrophic transitions between alternative and often markedly different states. The phenomenon of critical slowing down (CSD) can be used to anticipate such transitions…

Current early warning signs for tipping points often fail to distinguish between catastrophic shifts and less dramatic state changes, such as spatial pattern formation. This paper introduces a novel method that addresses this limitation by…

Finite-size scaling is a key tool in statistical physics, used to infer critical behavior in finite systems. Here we use the analogous concept of finite-time scaling to describe the bifurcation diagram at finite times in discrete dynamical…

Tipping points have been actively studied in various applications as well as from a mathematical viewpoint. A main technique to theoretically understand early-warning signs for tipping points is to use the framework of fast-slow stochastic…

Early-warning indicators (increase of autocorrelation and variance) are commonly applied to time series data to try and detect tipping points of real-world systems. The theory behind these indicators originates from approximating the…

Noise-induced transitions between metastable fixed points in systems evolving on multiple time scales are analyzed in situations where the time scale separation gives rise to a slow manifold with bifurcation. This analysis is performed…

Regime shifts are quite common in complex systems like cell regulations, disease transmissions, ecosystems, marine ice instability, etc. Several statistical indicators known as early warning signals (EWS) have been theorized to anticipate…

In a Nature article, Scheffer et al. presented a novel data-driven framework to predict critical transitions in complex systems. These transitions, which may stem from failures, degradation, or adversarial actions, have been attributed to…