Periodic synchronization in delayed memristive neural networks based on Filippov systems

In this paper, we consider the possibility to implement the periodic synchronization control of memristive neural networks with time-varying delay. On the one hand, we apply a new method based on Kakutani׳s fixed point theorem of set-valued maps to obtain the existence of periodic solutions for memristive neural networks. On the other hand, by designing novel discontinuous state-feedback controller and introducing some new analytic techniques, the drive-response structure of memristor-based neural networks with periodic coefficients can realize the p-type exponential complete synchronization. Moreover, the estimated rate of exponential synchronization depends on the time delay and system parameters. The analysis in this paper is performed via functional differential inclusions following the Filippov theory. Finally, the proposed design method and theoretical results are verified by numerical example with MATLAB programming.