ASYMPTOTIC STABILIZATION FOR DISCRETE TYPE STOCHASTIC DYNAMIC SYSTEM INCORPORATING DELAY

Abstract

This paper investigates the stability of differential equations of stochastic type by achieving the stability condition for the corresponding stochastic difference equation. By considering the stochastic differential equation that characterises the dynamics of a single isolated neurone involving delay, the system formulation is created. In order to discretise the stochastic differential equation, the Euler-Maruyama Method is utilised. And with the aid of theorems and appropriate assumptions, the desired stability is attained. To demonstrate the effectiveness of the proposed asymptotic stability result for the obtained theoretical results, we provide a numerical example.