相关论文: Synchronization of Coupled Stochastic Systems Driv…

We study the "periodic homogenization" for a class of nonlocal partial differential equations of parabolic-type with rapidly oscillating coefficients, related to stochastic differential equations driven by multiplicative isotropic…

These notes present an alternative approach to the asymptotic stability of stochastic partial differential equations driven by multiplicative noise, applicable to a wide range of dissipative systems. The method builds on general criteria…

We study the existence and uniqueness of solutions to stochastic differential equations with Volterra processes driven by L\'evy noise. For this purpose, we study in detail smoothness properties of these processes. Special attention is…

In this paper we investigate the numerical solution of stochastic partial differential equations (SPDEs) for a wider class of stochastic equations. We focus on non-diagonal colored noise instead of the usual space-time white noise. By…

We extend the taming techniques for explicit Euler approximations of stochastic differential equations (SDEs) driven by L\'evy noise with super-linearly growing drift coefficients. Strong convergence results are presented for the case of…

In this paper, we study a class of stochastic partial differential equations (SPDEs) driven by space-time fractional noises. Our method consists in studying first the nonlocal SPDEs and showing then the convergence of the family of these…

Recently, in a paper by Jentzen and Kloeden [Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 465 (2009) 649-667], a new method for simulating nearly linear stochastic partial differential equations (SPDEs) with additive noise has been…

Semilinear hyperbolic stochastic partial differential equations (SPDEs) find widespread applications in the natural and engineering sciences. However, the traditional Gaussian setting may prove too restrictive, as phenomena in mathematical…

A universal mechanism underlying generalized synchronization conditions in unidirectionally coupled stochastic oscillators is considered. The consideration is carried out in the framework of a modified system with additional dissipation.…

We consider synchronization by noise for stochastic partial differential equations which support traveling pulse solutions, such as the FitzHugh-Nagumo equation. We show that any two pulse-like solutions which start from different positions…

In this paper, we establish a large deviation principle for a type of stochastic partial differential equations (SPDEs) with locally monotone coefficients driven by L\'evy noise. The weak convergence method plays an important role.

Synchronization of identical chaotic systems subjected to common noise has been the subject of recent research. Studies on several chaotic systems have shown that, the synchronization is actually induced by the non-zero mean of the noise,…

In this paper, we study the stochastic logrithmic Schr\"odinger equation with saturated nonlinear multiplicative L\'evy noise. The global well-posedness is established for the stochastic logrithmic Schr\"odinger equation in an appropriate…

We present a novel idea for a coupling of solutions of stochastic differential equations driven by L\'{e}vy noise, inspired by some results from the optimal transportation theory. Then we use this coupling to obtain exponential…

We investigate common-noise-induced phase synchronization between uncoupled identical Hele-Shaw cells exhibiting oscillatory convection. Using the phase description method for oscillatory convection, we demonstrate that the uncoupled…

A standard approach to analysis of noise-induced effects in stochastic dynamics assumes a Gaussian character of the noise term describing interaction of the analyzed system with its complex surroundings. An additional assumption about the…

Recently, extracting data-driven governing laws of dynamical systems through deep learning frameworks has gained a lot of attention in various fields. Moreover, a growing amount of research work tends to transfer deterministic dynamical…

In the present work, we establish the approximation of nonlinear stochastic partial differential equation (SPDE) driven by cylindrical {\alpha}-stable L\'evy processes via modulation or amplitude equations. We study SPDEs with a cubic…

We show two examples of noise--induced synchronization. We study a 1-d map and the Lorenz systems, both in the chaotic region. For each system we give numerical evidence that the addition of a (common) random noise, of large enough…

We investigate bifurcation phenomena between slow and fast convergences of synchronization errors arising in the proposed synchronization system consisting of two identical nonlinear dynamical systems linked by a common noisy input only.…