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This article studies typical dynamics and fluctuations for a slow-fast dynamical system perturbed by a small fractional Brownian noise. Based on an ergodic theorem with explicit rates of convergence, which may be of independent interest, we…
This contribution investigates an original stochastic approach for the emergence of stop-and-go waves in traffic flow, a collective phenomenon with significant safety and environmental implications. Using a stable nonlinear car-following…
The effects of noise on the dynamics of nonlinear systems is known to lead to many counter-intuitive behaviors. Using simple planar limit cycle oscillators, we show that the addition of moderate noise leads to qualitatively different…
Important effects of noise on a one-dimensional gene expression model involving a single gene have recently been discussed. However, few works have been devoted to the transition in two-dimensional models which include the interaction of…
We investigate the influence of intrinsic noise on stable states of a one-dimensional dynamical system that shows in its deterministic version a saddle-node bifurcation between monostable and bistable behaviour. The system is a modified…
Transient properties of different physical systems with metastable states perturbed by external white noise have been investigated. Two noise-induced phenomena, namely the noise enhanced stability and the resonant activation, are…
When a physical system evolves in a thermal bath at a constant temperature, it arrives eventually to an equilibrium state whose properties are independent of the kinetic parameters and of the precise evolution scenario. This is generically…
The over-damped motion of a Brownian particle in an asymmetric, bistable, fluctuating potential shows noise induced stability: For intermediate fluctuation rates the mean occupancy of minima with an energy above the absolute minimum is…
We propose a new model in order to study behaviors of self-organized system such as a group of animals. We assume that the individuals have two degrees of freedom corresponding one to their internal state and the other to their external…
Many physical systems characterized by nonlinear multiscale interactions can be effectively modeled by treating unresolved degrees of freedom as random fluctuations. However, even when the microscopic governing equations and qualitative…
We consider the dynamics of a population of organisms containing two mutually inhibitory gene regulatory networks, that can result in a bistable switch-like behaviour. We completely characterize their local and global dynamics in the…
Stochastic resetting and noise-enhanced stability are two phenomena which can affect the lifetime and relaxation of nonequilibrium states. They can be considered as measures of controlling the efficiency of the completion process when a…
This paper studies a stochastic mean-field linear-quadratic optimal control problem with random coefficients. The state equation is a general linear stochastic differential equation with mean-field terms $\EE X(t)$ and $\EE u(t)$ of the…
Transitions between multiple stable states of nonlinear systems are ubiquitous in physics, chemistry, and beyond. Two types of behaviors are usually seen as mutually exclusive: unpredictable noise-induced transitions and predictable…
We introduce a class of exactly solvable models which exhibit an ordering noise-induced phase transition driven by an entropic mechanism. In contrast with previous studies, order does not appear in this case as a result of an instability of…
Complex dynamical systems which are governed by anomalous diffusion often can be described by Langevin equations driven by L\'evy stable noise. In this article we generalize nonlinear stochastic differential equations driven by Gaussian…
Turbulence transition often arises from a subcritical transition between bistable states characterized by invariant sets of deterministic dynamical systems, and such transitions can be triggered by system noise as rare events. In this…
In this paper we introduce a new class of state space models based on shot-noise simulation representations of non-Gaussian L\'evy-driven linear systems, represented as stochastic differential equations. In particular a conditionally…
We recently proposed a method for estimation of states and parameters in stochastic differential equations, which included intermediate time points between observations and used the Laplace approximation to integrate out these intermediate…
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…