Adaptive exponential synchronization in mean square for Markovian jumping neutral-type coupled neural networks with time-varying delays by pinning control

In this paper, the adaptive exponential synchronization problem of neutral-type coupled neural networks with Markovian switching parameters is investigated. The switching parameters are modeled as a continuous time, finite state Markov chain. Based on Lyapunov stability theory, stochastic analysis and matrix theory, some sufficient conditions for exponential synchronization in mean square are derived. The adaptive controllers are added to part of nodes, and the adaptive laws are depend on Markov chain and error states. Two numerical examples are exhibited to illustrate the validity of the theoretical results. Through the comparison of average value of synchronization control cost and synchronization time, we verify that control different nodes may be more effectively to achieve synchronization than control fixed nodes when the network topology is switching by a Markov chain.