Regularity of pullback attractors for non-autonomous stochastic FitzHugh-Nagumo systems with additive noises on unbounded domains

2014/11/28 by Wenqiang Zhao, Zhao, Wenqiang
Computer Science · Economics, Econometrics and Finance · Engineering · #35B40 #35B41 #35R60 #60H15 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #Stability and Controllability of Differential Equations #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1411.7743

openalex publication_date 2014/11/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove the existences of pullback attractors in L^p(ℝ^N)× L²(ℝ^N) for stochastic Fitzhugh-Nagumo system driven by both additive noises and deterministic non-autonomous forcings. The nonlinearity is polynomial like growth with exponent p-1. The asymptotic compactness for the cocycle in L^p(ℝ^N)× L²(ℝ^N) is proved by using asymptotic a priori method, where the plus and minus signs of the nonlinearity at large value are not required.

Citations

• Random dynamical systems
• Impulses and Physiological States in Theoretical Models of Nerve Membrane

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