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

摘要

The paper is devoted to the study of the dynamical behavior of the solutionsof stochastic FitzHugh-Nagumo lattice equations, driven by fractional Brownianmotions, with Hurst parameter greater than $1/2$. Under some usualdissipativity conditions, the system considered here features differentdynamics from the same one perturbed by Brownian motion. In our case, therandom dynamical system has a unique random equilibrium, which constitutes asingleton sets random attractor.