Multi-mode function synchronization of memristive neural networks with mixed delays and parameters mismatch via event-triggered control

Abstract

As we know, the study of complete synchronization of dynamic systems is usually confined to exponential synchronization and power-rate synchronization. Therefore, it is an interesting topic whether there are other complete synchronization methods or give a unified mathematical expression of these complete synchronization types. In this paper, we look into the issue of multi-mode function synchronization (MMFS) for memristive neural networks (MNNs) with two kinds of time-varying delays via event-triggered control. Two types of parameters mismatch in MNNs are considered. One is state-dependent, and by formulating a new Lyapunov functional, we achieve a sufficient criterion for the drive and response MNNs to synchronize in the form of convergence-like function L(t). The other is structure-dependent, which can only realize multi-mode function quasi-synchronization (MMFQS). Matrix measure method and a modified Halanay inequality are used to fulfill the multi-mode function quasi-synchronization between the drive and response MNNs. Conclusively, two numerical examples are simulated to prove the effectiveness of our theoretical results.