Existence of periodic measures of fractional stochastic delay FitzHugh-Nagumo systems on ℝ n

This article is concerned with periodic measures of fractional stochastic Fitzhugh-Nagumo systems with variable time delay defined on unbounded domains. First, we derive uniform estimates of solutions. Second, we establish the equicontinuity of solutions in probability that is used for proving the tightness of distributions of solutions. Then, we deduce the uniform estimates on the tails of solutions in probility in order to overcome the issue of non-compactness of Sobolev embeddings on unbounded domains. Finally, we demonstrate the existence of periodic measures by utilizing the Ascoli-Arzelà theorem and Krylov-Bogolyubov′s method.