Almost surely exponential stability of neural networks with Lévy noise and Markovian switching

In this brief, the problem of almost surely exponential stability analysis is considered for neural networks with Lévy noise and Markovian switching. The switching parameters are generated from a continuous-time irreducible Markov chain taking value in a finite-state space. The purpose of the problem addressed is to derive a sufficient condition such that the dynamics of the neural network is almost surely exponentially stable. By generalized Itô׳s formula, strong law of large numbers for martingales and ergodicity of Markov chain, the stochastic analysis approach is developed to establish the desired condition which depends only on the stationary distribution of the Markov chain and some constants. Two numerical examples are given to verify the usefulness of the stability condition.