Related papers: Early-warning indicators in the dynamic regime

Sudden transitions in the state of a system are often undesirable in natural and human-made systems. Such transitions under fast variation of system parameters are called rate-induced tipping. We experimentally demonstrate rate-induced…

Early stopping is a widely used technique to prevent poor generalization performance when training an over-expressive model by means of gradient-based optimization. To find a good point to halt the optimizer, a common practice is to split…

An increasing body of research focuses on using neural networks to model time series. A common assumption in training neural networks via maximum likelihood estimation on time series is that the errors across time steps are uncorrelated.…

We theoretically study divergent fluctuations of dynamical events at non-ergodic transitions. We first focus on the finding that a non-ergodic transition can be described as a saddle connection bifurcation of an order parameter for a time…

Change-point detection methods are proposed for the case of temporary failures, or transient changes, when an unexpected disorder is ultimately followed by a readjustment and return to the initial state. A base distribution of the…

We consider the effect on tipping from an additive periodic forcing in a canonical model with a saddle node bifurcation and a slowly varying bifurcation parameter. Here tipping refers to the dramatic change in dynamical behavior…

In this article, we study sequential change-point methods for discretely observed generalized Ornstein-Uhlenbeck processes with periodic drift. Two detection methods are proposed, and their respective performance is studied through…

Anticipating tipping points in complex systems is a fundamental challenge across domains. Traditional early warning signals (EWSs) based on critical slowing down, such as increasing sample variance, are widely used, but their ability to…

Bifurcations mark qualitative changes of long-term behavior in dynamical systems and can often signal sudden ("hard") transitions or catastrophic events (divergences). Accurately locating them is critical not just for deeper understanding…

The use of an Ornstein-Uhlenbeck (OU) process is ubiquitous in business, economics and finance to capture various price processes and evolution of economic indicators exhibiting mean-reverting properties. When structural changes happen,…

A wide variety of physical systems ranging from the firing of neurons to eutrophication of lakes to the presence of Arctic summer sea ice exhibit a phenomenon known as tipping. In mathematical models, tipping can be caused by bifurcations,…

Thanks to high-tech measurement systems like sensors, data are often collected with high frequency in modern industrial processes. This phenomenon could potentially produce autocorrelated and cross-correlated measurements. It has been shown…

Vector autoregressive (VAR) models are widely used in multivariate time series analysis for describing the short-time dynamics of the data. The reduced-rank VAR models are of particular interest when dealing with high-dimensional and highly…

Many natural systems undergo critical transitions, i.e. sudden shifts from one dynamical regime to another. In the climate system, the atmospheric boundary layer can experience sudden transitions between fully turbulent states and…

We study a two-dimensional low-dissipation dynamical system with a control parameter that is swept linearly in time across a transcritical bifurcation. We investigate the relaxation time of a perturbation applied to a variable of the system…

Many natural and man-made systems are prone to critical transitions -- abrupt and potentially devastating changes in dynamics. Deep learning classifiers can provide an early warning signal (EWS) for critical transitions by learning generic…

We investigate bifurcation phenomena between slow and fast convergences of synchronization errors arising in the proposed synchronization system consisting of two identical nonlinear dynamical systems linked by a common noisy input only.…

We consider discrete-time one-dimensional random dynamical systems with bounded noise, which generate an associated set-valued dynamical system. We provide necessary and sufficient conditions for a discontinuous bifurcation of a minimal…

Drawing upon the bursting mechanism in slow-fast systems, we propose indicators for the prediction of such rare extreme events which do not require a priori known slow and fast coordinates. The indicators are associated with functionals…

This article introduces a novel Bayesian method for asynchronous change-point detection in multivariate time series. This method allows for change-points to occur earlier in some (leading) series followed, after a short delay, by…