Synchronization for arrays of coupled jumping delayed neural networks and its application to image encryption

This paper deals with asynchronous synchronization for two arrays of coupled jumping neural networks with both a constant leakage delay and discrete time-varying delays in a master-slave configuration, where jumping instants of network modes and controller modes are asynchronous. The asynchronous control, which is governed by a finite piecewise homogeneous Markov process and involves the leakage delay and the bounds of the time-varying delays, is proposed. The resultant synchronization error system becomes a piecewise homogeneous Markovian jump nonlinear system with delays. The synchronization controllers are obtained based on the established stability criteria on the synchronization error system. Finally, a numerical example is provided to demonstrate the theoretical analysis and an image encryption algorithm based on the synchronized drive-response complex networks is also proposed.