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Random attractors for non-autonomous stochastic FitzHugh-Nagumo systems with multiplicative noise

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  • In this paper, we prove the existence and uniqueness of random attractors for the FitzHugh-Nagumo system defined on $\mathbb{R}^n$ driven by both deterministic non-autonomous forcing and multiplicative noise. The periodicity of random attractors is established when the system is perturbed by time periodic forcing. We also prove the upper semicontinuity of random attractors when the intensity of noise approaches zero.
    Mathematics Subject Classification: Primary: 37L55; Secondary: 37L30, 35R60, 60H15.


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