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The random attractor of stochastic Fitzhugh-Nagumo equations in an infinite lattice with white noises. (English) Zbl 1126.37048

Summary: The present paper is devoted to the existence of a random attractor for the stochastic FitzHugh-Nagumo equations in an infinite lattice with additive white noise. Using the Ornstein-Uhlenbeck transform, we firstly show the existence of an absorbing set, then we prove that the random dynamical system is asymptotically compact. Finally, the existence of the random attractor is provided.

MSC:

37L30 Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems
35K57 Reaction-diffusion equations
35B41 Attractors
37H10 Generation, random and stochastic difference and differential equations
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