Existence and global exponential stability of Weyl almost automorphic solution in finite dimensional distributions for SDINNs

Abstract

This article mainly studies the existence and stability of Weyl almost automorphic solutions in finite dimensional distributions to stochastic delayed inertial neural networks (SDINNs). Since the family consisting of Weyl almost automorphic stochastic processes is not closed under linear operations, we first utilising the Hölder inequality, the Burkholder Davis Gundy inequality, and the Banach fixed point principle to prove that the considered system admits a unique L p -bounded and L p -uniformly continuous solution. Then, we used the definition to prove that this solution is also Weyl almost automorphic in finite dimensional distributions. In addition, we utilise the method of proof by contradiction combined with inequality skills to show the global exponential stability in pth mean of the Weyl almost automorphic solution. Finally, we confirm the validity of our results through a numerical example and computer simulation.