Finite fractal dimensions of random attractors for stochastic FitzHugh–Nagumo system with multiplicative white noise

In this paper, we consider the asymptotic behavior of solutions for stochastic non-autonomous FitzHugh–Nagumo system with multiplicative white noise. First we prove the existence of random attractor of the random dynamical system generated by the solutions of considered system. Then we present some conditions for estimating an upper bound of the fractal dimension of a random invariant set of a random dynamical system on a separable Banach space and apply these conditions to prove the finiteness of fractal dimension of random attractor.