Adaptive fixed-time synchronization of stochastic memristor-based neural networks with discontinuous activations and mixed delays

Abstract

In this paper, adaptive fixed-time synchronization(FTS) of stochastic memristor-based neural networks(MNNs) with discontinuous activations and mixed delays is investigated. Both continuous and discontinuous activation functions are discussed for stochastic MNNs. Meanwhile, a feedback control strategy and a new adaptive control strategy are proposed to ensure FTS of stochastic MNNs. Since the MNNs are right-hand discontinuous systems, the set-valued mapping and differential inclusion theory are used to deal with its discontinuity. Synchronization criteria and the settling time (ST) are obtained with the aid of some lemmas and mathematical inequalities under corresponding control schemes. It’s worth noting that the ST can be adjusted to desired value by controller parameters regardless of the initial values. Finally, the feasibility of theoretical results are proved via simulation results.