Work

Weak Mean Attractors of Fractional Stochastic Lattice Systems Driven by Nonlinear Delay Noise

Year: 2024

Type: article

Abstract: This paper deals with the existence and uniqueness of weak pullback mean random attractors for fractional stochastic lattice systems driven by nonlinear delay noise defined on the entire integer set \(\mathbb{Z}\). We first establish the global well-posedness to stochastic lattice system in \(C([\tau,\infty), L^2(\Omega, \ell^2))\) when the nonlinear diffusion terms and drift terms are locally Lipschitz continuous functions. Then we define a mean random dynamical system through the solution operators and prove the existence and uniqueness of weak pullback mean random attractors in \(L^2(\Omega,\mathcal{F};\ell^2)\times L^2\big(\Omega,\mathcal{F};L^2((-\rho,0), \ell^2)\big)\) under certain conditions.

Source: Electronic Journal of Applied Mathematics

DOI: 10.61383/ejam.20242485

Authors: Ailin Bai, Pengyu Chen

Institution: Northwest Normal University

Language: English

Topic: Stability and Controllability of Differential Equations

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: diamond

Funders: Northwest Normal University, National Natural Science Foundation of China

Awards: G3311631959, G3380324188