Weyl Almost Automorphic Oscillation in Finite-Dimensional Distributions to Stochastic SICNNs with D Operator

Abstract

In this article, we first propose a reasonable definition of Weyl almost automorphic stochastic process in finite-dimensional distributions. Then, efforts were made to investigate the existence and stability of Weyl almost automorphic solutions in finite-dimensional distributions to a class of stochastic shunting inhibitory cellular neural networks (SICNNs) with D operators. Because the space formed by Weyl almost automorphic random processes is not a complete space, in order to overcome this difficulty, firstly, we use Banach’s fixed point theorem on a closed subset of the Banach space composed of \(\mathcal {L}^p\) bounded and \(\mathcal {L}^p\) uniformly continuous random processes to obtain that the network under consideration admits a unique solution in this subset, secondly, based on the definition of Weyl almost automorphic solutions in finite-dimensional distributions, using inequality techniques, we prove that the solution is also Weyl almost automorphic in finite-dimensional distributions, then, the global exponential stability of the Weyl almost automorphic solution is proved using the contradiction method. The results and methods of this paper are new and can be used to study the corresponding problems of other neural network models. Finally, a numerical example is provided to demonstrate the effectiveness of our results.