Periodic measures of impulsive stochastic neural networks lattice systems with delays

Abstract

This paper is concerned with the periodic measures of a class of periodic stochastic neural networks lattice models with delays and nonlinear impulses. First, by employing the idea of uniform estimates on the tails of the solutions, the technique of diadic division, and generalized Ascoli–Arzela theorem, we prove the tightness of a family of distributions of the segment solutions of the lattice systems. Then, the existence of periodic measures is established by using the Krylov–Bogolyubov method.