Multisynchronization of Coupled Multistable Neural Networks via Event-Triggered Impulsive Control and Its Application to Associative Memory

This article studies multisynchronization of coupled multistable neural networks (NNs) with directed topology viaevent-triggered impulsive (ETI) control. At first, the activation function (AF) with 2p corners is proposed and it is proved thatann-neuron subnetwork can produce(p+1)n locally stableequilibrium points (EPs) or periodic orbits (POs) under somecriteria. Furthermore, to achieve multisynchronization, an ETI controller is designed. Compared with conventional impulsivecontrol strategy, ETI control strategy proposed in this paper can reduce the communication cost and save the bandwidth.Sufficient conditions are given to ensure both dynamical multisynchronization (DMS) and static multi synchronization(SMS) of coupled neural networks (CNNs) with fixed and switching topologies. Moreover, it is proved that the Zenobehavior can be avoided. Lastly, two examples and the application to associative memory are illustrated to testify the validity of the obtained results.