Singleton sets random attractor for stochastic FitzHugh–Nagumo lattice equations driven by fractional Brownian motions

• A model of stochastic FitzHugh–Nagumo lattice equations driven by fBm was proposed.
• The model driven by fBm generates a random dynamical system in ℓ2×ℓ2ℓ2×ℓ2.
• The random dynamical system has a singleton sets random attractor.

The paper is devoted to the study of the dynamical behavior of the solutions of stochastic FitzHugh–Nagumo lattice equations, driven by fractional Brownian motions, with Hurst parameter greater than 1/2. Under some usual dissipativity conditions, the system considered here features different dynamics from the same one perturbed by Brownian motion. In our case, the random dynamical system has a unique random equilibrium, which constitutes a singleton sets random attractor.