Exponential Stability of Stochastic Delayed Neural Networks with Inverse Hölder Activation Functions and Markovian Jump Parameters

Abstract

The exponential stability issue for a class of stochastic neural networks (SNNs) with Markovian jump parameters, mixed time delays, and α-inverse Hölder activation functions is investigated. The jumping parameters are modeled as a continuous-time finite-state Markov chain. Firstly, based on Brouwer degree properties, the existence and uniqueness of the equilibrium point for SNNs without noise perturbations are proved. Secondly, by applying the Lyapunov-Krasovskii functional approach, stochastic analysis theory, and linear matrix inequality (LMI) technique, new delay-dependent sufficient criteria are achieved in terms of LMIs to ensure the SNNs with noise perturbations to be globally exponentially stable in the mean square. Finally, two simulation examples are provided to demonstrate the validity of the theoretical results.