Square-mean almost automorphic solution of a stochastic cellular neural network on time scales
Soniya Dhama, Syed Haider Abbas · Journal of Integral Equations and Applications · 2020
We derive some sufficient conditions for the existence of a square-mean almost automorphic solution for a stochastic cellular neural network on time scales by using Krasnoselskii’s fixed point theorem. The Banach contraction principle is also used to show the uniqueness of a solution with some additional restrictions. Exponential stability of the obtained solution is also discussed by taking a suitable Lyapunov functional on time scale. At the end, we give a numerical example to illustrate the effectiveness of the obtained theoretical results. Our results are valid for general time scale, and the cases 𝕋=ℝ or ℤ are particular cases.