Abstract
This paper is concerned with the asymptotic behavior of solutions for a class of non-autonomous fractional FitzHugh-Nagumo equations deriven by additive white noise. We first provide some sufficient conditions for the existence and uniqueness of solutions, and then prove the existence and uniqueness of tempered pullback random attractors for the random dynamical system generated by the solutions of considered equations in an appropriate Hilbert space. The proof is based on the uniform estimates and the decomposition of dynamical system.
Highlights
In this paper, we investigate the random attractor of the non-autonomous stochastic fractional FitzHugh-Nagumo equations with additive white noise in bounded domains
This paper is concerned with the asymptotic behavior of solutions for a class of non-autonomous fractional FitzHugh-Nagumo equations deriven by additive white noise
We first provide some sufficient conditions for the existence and uniqueness of solutions, and prove the existence and uniqueness of tempered pullback random attractors for the random dynamical system generated by the solutions of considered equations in an appropriate Hilbert space
Summary
We investigate the random attractor of the non-autonomous stochastic fractional FitzHugh-Nagumo equations with additive white noise in bounded domains. The fractional FitzHugh-Nagumo monodomain model is presented, the model consists of a coupled fractional nonlinear reaction-diffusion model and a system of ordinary differential equations. On the other hand, comparing with [15], we are concerned with the existence of random attractors of the fractional FitzHugh-Nagumo equation on U driven by additive noise rather than multiplicative noise, so new difficulties arise from the estimates for some terms, especially the nonlinearity f.
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