The random attractor of stochastic FitzHugh–Nagumo equations in an infinite lattice with white noises

The present paper is devoted to the existence of the random attractor of 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 prove that the random dynamical system is asymptotically compact. Finally, the existence of the random attractor is provided.