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In stochastic resonance, a periodically forced Brownian particle in a double-well potential jumps between minima at rare increments, the prediction of which poses a major theoretical challenge. Here, we use a path-integral method to find a…

There is a growing awareness that catastrophic phenomena in biology and medicine can be mathematically represented in terms of saddle-node bifurcations. In particular, the term `tipping', or critical transition has in recent years entered…

A snap-through bifurcation occurs when a bistable structure loses one of its stable states and moves rapidly to the remaining state. For example, a buckled arch with symmetrically clamped ends can snap between an inverted and a natural…

In this article it is proved that the dynamical properties of a broad class of semilinear parabolic problems are sensitive to arbitrarily small but smooth perturbations of the nonlinear term, when the spatial dimension is either equal to…

In many plasma systems, introducing a small background shear flow is enough to stabilize the system linearly. The nonlinear dynamics are much less sensitive to sheared flows than the average linear growthrates, and very small amplitude…

Ecosystems tend to fluctuate around stable equilibria in response to internal dynamics and environmental factors. Occasionally, they enter an unstable tipping region and collapse into an alternative stable state. Our understanding of how…

Nonlinear and non-stationary processes are prevalent in various natural and physical phenomena, where system dynamics can change qualitatively due to bifurcation phenomena. Traditional machine learning methods have advanced our ability to…

We analyze the properties of arguably the simplest bilinear stochastic multiplicative process, proposed as a model of financial returns and of other complex systems combining both nonlinearity and multiplicative noise. By construction, it…

In this work, we analyse the effect of adding Gaussian white noise to the slow variable of a slow--fast system passing through a saddle--node (or fold) bifurcation. This problem is mainly motivated by applications to non-equilibrium energy…

We propose a topological framework for the detection of Hopf bifurcations directly from time series, based on persistent homology applied to phase space reconstructions via Takens embedding within the framework of Topological Data Analysis.…

A main puzzle of deep networks revolves around the absence of overfitting despite large overparametrization and despite the large capacity demonstrated by zero training error on randomly labeled data. In this note, we show that the dynamics…

Characterization of equilibrium topological quantum phases by non-equilibrium quench dynamics provides a novel and efficient scheme in detecting topological invariants defined in equilibrium. Nevertheless, most of the previous studies have…

A weakly nonlinear study is numerically conducted to determine the behaviour near the onset of convection in rotating spherical shells. The mathematical and numerical procedure is described in generality, with the results presented for an…

Detecting early warning indicators for abrupt dynamical transitions in complex systems or high-dimensional observation data is essential in many real-world applications, such as brain diseases, natural disasters, and engineering…

Human activity is leading to changes in the mean and variability of climatic parameters in most locations around the world. The changing mean has received considerable attention from scientists and climate policy makers. However, recent…

Abrupt transitions are a central concern in climate and ecological research, and may arise when critical thresholds known as tipping points are crossed. However, previous work has shown that finite-time overshoots of tipping points can be…

Linear stability analysis currently fails to predict turbulence transition in canonical viscous flows. We show that two alternative models of the boundary condition for incipient perturbations at solid walls produce linear instabilities…

This paper investigates the dynamic behavior of a simplified single reed instrument model subject to a stochastic forcing of white noise type when one of its bifurcation parameters (the dimensionless blowing pressure) increases linearly…

Multistability is a ubiquitous feature in systems of geophysical relevance and provides key challenges for our ability to predict a system's response to perturbations. Near critical transitions small causes can lead to large effects and -…

Noise is usually regarded as adversarial to extract the effective dynamics from time series, such that the conventional data-driven approaches usually aim at learning the dynamics by mitigating the noisy effect. However, noise can have a…