Stability for delayed Markovian switched stochastic neural networks with jump in a phase space

Abstract

In this paper, we interest by stochastic stability and stochastic asymptotic stability for a kind of delayed stochastic neutral networks with Markovian switching driven by Lévy noise in the phase space $C^{\mu}$. Our approach is based on the M-matrix theory, Lyapunov method, some properties of phase space and stochastic analysis technique. Our results generalize some existing ones. Under some new sufficient conditions in terms of the coefficients of the model, stochastic stability and stochastic asymptotic stability to system are shown in the considerate phase space. One example is given to illustrate the usefulness of the theoretical theorem.