Adaptive synchronization of delayed Markovian switching neural networks with Lévy noise

The problem of adaptive synchronization is considered for stochastic delayed neural networks with Markovian switching and Lévy noise. The aim of the problem is to derive a sufficient condition and an adaptive control strategy such that the synchronization can be achieved for the master system and the slave system. By generalized Itô׳s formula and Lyapunov functional method, a sufficient condition in terms of LMI is established to ensure the synchronization of the two systems, and the adaptive update law is determined as well. A numerical simulation is provided to verify the usefulness of the proposed criterion.