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June 2018, 23(4): 1689-1720. doi: 10.3934/dcdsb.2018072
Asymptotic behavior of random fitzhugh-nagumo systems driven by colored noise
Anhui Gu 1, and Bixiang Wang 2,
School of Mathematics and Statistics, Southwest University, Chongqing 400715, China
Department of Mathematics, New Mexico Institute of Mining and Technology, Socorro, NM 87801, USA
Received July 2017 Revised August 2017 Published January 2018
Fund Project: The first author was supported by China Scholarship Council (No. 201608505082)
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In this paper, we prove the existence and uniqueness of random attractors for the FitzHugh-Nagumo system driven by colored noise with a nonlinear diffusion term. We demonstrate that the colored noise is much easier to deal with than the white noise for studying the pathwise dynamics of stochastic systems. In addition, we show the attractors of the random FitzHugh-Nagumo system driven by a linear multiplicative colored noise converge to that of the corresponding stochastic system driven by a linear multiplicative white noise.
Keywords: Random attractor, colored noise, white noise, FitzHugh-Nagumo system.
Mathematics Subject Classification: Primary: 35B40, 35B41; Secondary: 37L30.
Citation: Anhui Gu, Bixiang Wang. Asymptotic behavior of random fitzhugh-nagumo systems driven by colored noise. Discrete & Continuous Dynamical Systems - B, 2018, 23 (4) : 1689-1720. doi: 10.3934/dcdsb.2018072
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Anhui Gu Bixiang Wang