Related papers: The dynamic saddle-node bifurcation with noise on …

In oscillatory reaction-diffusion systems, time-delay feedback can lead to the instability of uniform oscillations with respect to formation of standing waves. Here, we investigate how the presence of additive, Gaussian white noise can…

Traffic flow oscillations, including traffic waves, are a common yet incompletely understood feature of congested traffic. Possible mechanisms include traffic flow instabilities, indifference regions or finite human perception thresholds…

Stochastic averaging allows for the reduction of the dimension and complexity of stochastic dynamical systems with multiple time scales, replacing fast variables with statistically equivalent stochastic processes in order to analyze…

We explore sequential escape behaviour of coupled bistable systems under the influence of stochastic perturbations. We consider transient escapes from a marginally stable "quiescent" equilibrium to a more stable "active" equilibrium. The…

The noise-enhanced trapping is a surprising phenomenon that has already been studied in chaotic scattering problems where the noise affects the physical variables but not the parameters of the system. Following this research, in this work…

We establish a slow manifold for a fast-slow stochastic evolutionary system with anomalous diffusion, where both fast and slow components are influ- enced by white noise. Furthermore, we prove the exponential tracking property for the…

We investigate the role of noise in the phenomenon of stochastic synchronization of switching events in a rocked, overdamped bistable potential driven by white Gaussian noise, the archetype description of Stochastic Resonance. We present a…

We study the effects of noise cross-correlations on the steady states of driven, nonequilibrium systems, which are described by two stochastically driven dynamical variables, in one dimension. We use a well-known stochastically driven…

We report a noise induced delay of bifurcation in a simple pulse-coupled neural circuit. We study the behavior of two neural oscillators, each individually governed by saddle-node dynamics, with reciprocal excitatory synaptic connections.…

Studies about the constructive aspects of noise and fluctuations in different non-linear systems have shown that the addition of external noise to systems with an intrinsic noise may result in a less noisy response. Recently, the…

Some systems cannot be predicted by classical theories and it is required the development of combined deterministic and stochastic theories that make used of noise for dynamical prediction. Noise is not always an interfering signal which…

Stochastic resonance (SR) is a coherence enhancement effect due to noise that occurs in periodically-driven nonlinear dynamical systems. A very broad range of physical and biological systems present this effect such as climate change,…

We have analyzed the interplay between noise and periodic spatial modulations in bistable systems outside equilibrium and found that noise is able to increase the spatial order of the system, giving rise to periodic patterns which otherwise…

For a model nonlinear dynamical system, we show how one may obtain its bifurcation behavior by introducing noise into the dynamics and then studying the resulting Langevin dynamics in the weak-noise limit. A suitable quantity to capture the…

In recent years, the hardware implementation of neural networks, leveraging physical coupling and analog neurons has substantially increased in relevance. Such nonlinear and complex physical networks provide significant advantages in speed…

The ability of Gaussian noise to induce ordered states in dynamical systems is here presented in an overview of the main stochastic mechanisms able to generate spatial patterns. These mechanisms involve: (i) a deterministic local dynamics…

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…

Slow parameter drift is common in many systems (e.g., the amount of greenhouse gases in the terrestrial atmosphere is increasing). In such situations, the attractor on which the system trajectory lies can be destroyed, and the trajectory…

The synchronized phase of globally coupled nonlinear oscillators subject to noise fluctuations is studied by means of a new analytical approach able to tackle general couplings, nonlinearities, and noise temporal correlations. Our results…

In this study, we explore the effects of including noise predictors and noise observations when fitting linear regression models. We present empirical and theoretical results that show that double descent occurs in both cases, albeit with…