Dynamical behaviors of non-autonomous fractional FitzHugh-Nagumo system driven by additive noise in unbounded domains

doi:10.1007/s11464-021-0896-7

Front. Math. China

2021, Vol. 16

Issue (1) : 59-93 https://doi.org/10.1007/s11464-021-0896-7

RESEARCH ARTICLE

Dynamical behaviors of non-autonomous fractional FitzHugh-Nagumo system driven by additive noise in unbounded domains

Chunxiao GUO¹, Yiju CHEN², Ji SHU³(

), Xinguang YANG⁴

¹. Department of Mathematics, China University of Mining and Technology, Beijing 100083, China
². Department of Mathematics, Sichuan University, Chengdu 610065, China
³. School of Mathematical Science, Laurent Mathematics Center and V. C. & V. R. Key Lab, Sichuan Normal University, Chengdu 610066, China
⁴. Department of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, China

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Abstract

The regularity of random attractors is considered for the nonautonomous fractional stochastic FitzHugh-Nagumo system. We prove that the system has a pullback random attractor that is compact in $H s (ℝ n) × L 2 (ℝ n)$ and attracts all tempered random sets of $L s (ℝ n) × L 2 (ℝ n)$ in the topology of $H s (ℝ n) × L 2 (ℝ n)$ with $s ∈ (0, 1)$ . By the idea of positive and negative truncations, spectral decomposition in bounded domains, and tail estimates, we achieved the desired results.

Keywords Fractional stochastic FitzHugh-Nagumo system random attractor asymptotic compactness

Corresponding Author(s): Ji SHU

Issue Date: 26 March 2021

Cite this article:

Chunxiao GUO,Yiju CHEN,Ji SHU, et al. Dynamical behaviors of non-autonomous fractional FitzHugh-Nagumo system driven by additive noise in unbounded domains[J]. Front. Math. China, 2021, 16(1): 59-93.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-021-0896-7
https://academic.hep.com.cn/fmc/EN/Y2021/V16/I1/59

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