Moment stability of McKean-Vlasov stochastic recurrent neural networks with mixed delays.

Abstract

This paper investigates a class of McKean-Vlasov stochastic recurrent neural networks (MV-SRNNs) incorporating both time-varying discrete and distributed delays. The system coefficients depend not only on the state of the underlying stochastic process but also on its probability distribution. Focusing on the existence of solutions and stability, we first prove the existence of mild solutions by using resolvent operator theory. Subsequently, we establish sufficient conditions in three distinct complete functional spaces (accounting for both bounded and unbounded delays) ensuring the existence, uniqueness, and stability of solutions. Finally, several examples are used to verify the applicability of the theoretical results in this paper.