S-asymptotically (ω, c)-periodic behavior of hybrid-time shunting inhibitory cellular neural networks with delays and stochastic perturbations

This paper investigates pth-mean S-asymptotically (ω, c)-periodic stochastic processes on periodic time scales and applies it to stochastic shunting-inhibitory cellular neural networks characterized by discrete time-varying delays and infinite distributed delays. In the presence of standard Lipschitz and growth conditions, as well as stochastic perturbations driven by a Wiener process, we examine the existence and uniqueness (pathwise) of pth-mean S-asymptotically (ω, c)-periodic solutions. Furthermore, we derive sufficient conditions for their pth-mean exponential stability. The analysis makes use of time scale calculus, a Banach space setup that is appropriate for the (ω, c)-weighted processes, fixed-point arguments, and estimates of the Burkholder-Davis-Gundy type inequality for the stochastic integrals on time scales. The results of the theoretical analysis are illustrated and validated through the use of numerical simulations on representative continuous, discontinuous, and nonuniform time scales.