Synchronization of neural networks with memristor-resistor bridge synapses and Lévy noise

Abstract In this paper, a kind of memristor-resistor bridge synapses are applied to neural networks, which makes the connection weights of networks continuously adjustable. A novel model for this new kind of neural networks is established, in which the memory characteristic of memristors is retained. The state synchronization of the model with the influence of Levy noise is investigated. By making use of the Ito formula for Levy process and Lyapunov method, a sufficient condition is obtained for exponentially state synchronization in mean square of the drive and response networks. Moreover, by applying controller to each synapse, the complete synchronization of the drive and response networks is achieved. Finally, numerical examples are carried out to illustrate the feasibility of theoretical results.