相关论文: Common noise pullback attractors for stochastic dy…
The aim of this contribution is to study the particle dynamics in a storage ring under the influence of noise. Some simplified stochastic beam dynamics problems are treated by solving the corresponding Fokker-Planck equations numerically.
The irreducibility is fundamental for the study of ergodicity of stochastic dynamical systems. The existing methods on the irreducibility of stochastic partial differential equations (SPDEs) and stochastic differential equations (SDEs)…
We have analyzed the effects of the addition of external noise to non-dynamical systems displaying intrinsic noise, and established general conditions under which stochastic resonance appears. The criterion we have found may be applied to a…
For pullback attractors of asymptotically autonomous dynamical systems we study the convergences of their components towards the global attractors of the limiting semigroups. We use some conditions of uniform boundedness of pullback…
Biological systems operate under persistent noise, which can alter system states and induce transitions between attractors. Here, we study the attractor dynamics of Boolean networks focusing on the transitions between attractors induced by…
Recently it has been found that different physical systems driven by identical random noise behave exactly identical after a long time. It is also suggested that this is an outcome of finite precision in numerical experiments. Here we show…
In this paper we present a general result with an easily checkable condition that ensures a transition from chaotic regime to regular regime in random dynamical systems with additive noise. We show how this result applies to a prototypical…
A general class of dynamical systems which can be trained to operate in classification and generation modes are introduced. A procedure is proposed to plant asymptotic stationary attractors of the deterministic model. Optimizing the…
The purpose of the present paper consists in proposing and discussing a double probabilistic representation for a porous media equation in the whole space perturbed by a multiplicative colored noise. For almost all random realizations…
Effect of noise in inducing order on various chaotically evolving systems is reviewed, with special emphasis on systems consisting of coupled chaotic elements. In many situations it is observed that the uncoupled elements when driven by…
Many systems in physics, engineering, and biology exhibit multiscale stochastic dynamics, where low-dimensional slow variables evolve under the influence of high-dimensional fast processes. In practice, observations are often limited to a…
We extend a model of positive feedback and contagion in large mean-field systems, by introducing a common source of noise driven by Brownian motion. Although the driving dynamics are continuous, the positive feedback effect can lead to…
McKean-Vlasov SDEs describe systems where the dynamics depend on the law of the process. The corresponding Fokker-Planck equation is a nonlinear, nonlocal PDE for the corresponding measure flow. In the presence of common noise and…
In this paper, we prove the existences of pullback attractors in $L^{p}(\mathbb{R}^N)\times L^{2}(\mathbb{R}^N)$ for stochastic Fitzhugh-Nagumo system driven by both additive noises and deterministic non-autonomous forcings. The…
A general approach to provide approximate parameterizations of the "small" scales by the "large" ones, is developed for stochastic partial differential equations driven by linear multiplicative noise. This is accomplished via the concept of…
We investigate the longtime behavior of stochastic partial differential equations (SPDEs) with differential operators that depend on time and the underlying probability space. In particular, we consider stochastic parabolic evolution…
This paper is a continuation of the paper \cite{JL}, which focuses on exploring the global stability of nonlinear stochastic feedback systems on the nonnegative orthant driven by multiplicative white noise and presenting a couple of…
This paper investigates the long-time dynamics of solutions for an abstract nonlinear stochastic hydrodynamic-type equation driven by multiplicative L\'{e}vy noise. The framework encompasses several key hydrodynamical models, including the…
In this paper, we investigate the uniform measure attractors of the distribution-dependent nonautonomous 2D stochastic Navier-Stokes equations driven by nonlinear noise and subject to almost periodic external forcing. Owing to the…
We prove the existence and uniqueness of tempered random attractors for stochastic Reaction-Diffusion equations on unbounded domains with multiplicative noise and deterministic non-autonomous forcing. We establish the periodicity of the…