Limiting dynamical behavior of random fractional FitzHugh-Nagumo systems driven by a Wong-Zakai approximation process

Dingshi Li; Xiaohu Wang; Junyilang Zhao

doi:10.3934/cpaa.2020120

Article Contents

2020, Volume 19, Issue 5: 2751-2776. Doi: 10.3934/cpaa.2020120

This issue Previous Article Asymptotic analysis for 1D compressible Navier-Stokes-Vlasov equations Next Article

$ L^{p(\cdot)} $

-regularity of Hessian for nondivergence parabolic and elliptic equations with measurable coefficients

Limiting dynamical behavior of random fractional FitzHugh-Nagumo systems driven by a Wong-Zakai approximation process

1.
School of Mathematics, Southwest Jiaotong University, Chengdu, Sichuan 610031, China
2.
National Engineering Laboratory of, Integrated Transportation Big Data Application Technology, Chengdu, Sichuan 610031, China
3.
Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, China

^* Corresponding author
^* Corresponding author

Received: March 31, 2019

Revised: August 31, 2019

Published: March 2020

The work is supported by NSFC (11601446, 11701475, 11871049, 11971394), Sichuan Science and Technology Program (2019YJ0215), and Open Research Fund for National Engineering Laboratory of Integrated Transportation Big Data Application Technology (CTBDAT201905)

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Abstract

In this paper, we study the long term behavior of non-autonomous fractional FitzHugh-Nagumo systems with random forcing given by an approximation of white noise, called Wong-Zakai approximation. We first prove the existence and uniqueness of tempered pullback attractors for the Wong-Zakai approximation fractional FitzHugh-Nagumo systems, and then establish the upper semicontinuity of attractors of system driven by a linear multiplicative Wong-Zakai approximations as random forcing approaches white noise in some sense.

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Mathematics Subject Classification: Primary: 35B40, 37L55; Secondary: 35B41, 37L30.

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