Random Attractor Of Stochastic FitzHugh-Nagumo Equations

The present paper is devoted to the existence of the random attractor of stochastic FitzHugh-Nagumo infinite lattice system with multiplicative white noise. Using the Ornstein-Uhlenbeck transform, the lattice system is transformed into a random differential equation with random coefficients ,which generate a Random Dynamical System. We firstly show the existence of a random bounded absorbing set. Then we prove that the random dynamical system is asymptotically compact. Finally, we prove the existence of the random attractor.