Related papers: Invariant foliations for stochastic dynamical syst…
Invariant foliations are geometric structures for describing and understanding the qualitative behaviors of nonlinear dynamical systems. For stochastic dynamical systems, however, these geometric structures themselves are complicated random…
Invariant manifolds are fundamental tools for describing and understanding nonlinear dynamics. In this paper, we present a theory of stable and unstable manifolds for infinite dimensional random dynamical systems generated by a class of…
This paper discerns the invariant manifold of a class of ill-posed stochastic evolution equations driven by a nonlinear multiplicative noise. To be more precise, we establish the existence of mean-square random unstable invariant manifold…
Invariant foliations are complicated random sets useful for describing and understanding the qualitative behaviors of nonlinear dynamical systems. We will consider invariant foliations for stochastic partial differential equation with…
Nonlinear dynamical systems are sometimes under the influence of random fluctuations. It is desirable to examine possible bifurcations for stochastic dynamical systems when a parameter varies. A computational analysis is conducted to…
This work aims at understanding the slow dynamics of a nonlocal fast-slow stochastic evolutionary system with stable Levy noise. Slow manifolds along with exponential tracking property for a nonlocal fast-slow stochastic evolutionary system…
This work is concerned with the dynamics of a class of slow-fast stochastic dynamical systems with non-Gaussian stable L\'evy noise with a scale parameter. Slow manifolds with exponentially tracking property are constructed, eliminating the…
The current paper is devoted to the asymptotic behavior of a class of stochastic PDE. More precisely, with the help of the theory of integrated semigroups and a crucial estimate of the random Stieltjes convolution, we study the existence…
We study stochastic bifurcation for a system under multiplicative stable Levy noise (an important class of non-Gaussian noise), by examining the qualitative changes of equilibrium states in its most probable phase portraits. We have found…
We use the version of the Lyapunov--Perron method operating on individual solutions to investigate the existence of invariant manifolds for non-autonomous dynamical systems, focusing in particular on inertial and stable manifolds. We…
Little seems to be known about the invariant manifolds for stochastic partial differential equations (SPDEs) driven by nonlinear multiplicative noise. Here we contribute to this aspect and analyze the Lu-Schmalfu{\ss} conjecture…
In this paper, we study the limiting behavior for stochastic differential equations driven by non-Gaussian alpha-stable Levy noise as alpha approaches 2. We first prove the convergence of solutions for system driven by alpha-stable Levy…
This work is concerned with existence of weak solutions to discon- tinuous stochastic differential equations driven by multiplicative Gaus- sian noise and sliding mode control dynamics generated by stochastic differential equations with…
Properties of systems driven by white non-Gaussian noises can be very different from these systems driven by the white Gaussian noise. We investigate stationary probability densities for systems driven by $\alpha$-stable L\'evy type noises,…
This work is about a slow-fast data assimilation system under non-Gaussian noisy fluctuations. Firstly, we show the existence of a random invariant manifold for a stochastic dynamical system with non-Gaussian noise and two-time scales.…
This article aims to investigate sufficient conditions for the stability of stochastic differential equations with a random structure, particularly in contexts involving the presence of concentration points. The proof of asymptotic…
The aim of this paper is to prove the existence and smoothness of stable and unstable invariant manifolds for a stochastic delayed partial differential equation of parabolic type. The stochastic delayed partial differential equation is…
This paper concerns the effects of additive non-Gaussian L\'evy noises on the pitchfork bifurcation. We consider two types of noises, $\alpha$-stable process and the truncated process. Under both $\alpha$-stable process and the truncated…
Given the significance of physical measures in understanding the complexity of dynamical systems as well as the noisy nature of real-world systems, investigating the stability of physical measures under noise perturbations is undoubtedly a…
This paper studies the finite-time stability and stabilization of linear discrete time-varying stochastic systems with multiplicative noise. Firstly, necessary and sufficient conditions for finite-time stability are presented via state…