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 via event-triggered impulsive (ETI) control. At first, the activation function (AF) with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${2p}$ </tex-math></inline-formula> corners is proposed and it is proved that an n-neuron subnetwork can produce <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${(p+1)^{n}}$ </tex-math></inline-formula> locally stable equilibrium points (EPs) or periodic orbits (POs) under some criteria. Furthermore, to achieve multisynchronization, an ETI controller is designed. Compared with conventional impulsive control 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 multisynchronization (SMS) of coupled neural networks (CNNs) with fixed and switching topologies. Moreover, it is proved that the Zeno behavior can be avoided. Lastly, two examples and the application to associative memory are illustrated to testify the validity of the obtained results. Note to Practitioners—ETI control could reduce the number of packets sent as well as the control cost compared with conventional impulsive control. In addition, combining impulsive control with event-triggered schemes into multisynchronization analysis of CNNs is challenging because of the large number of synchronization manifolds in CNNs. Therefore, this research studies multisynchronization of coupled multistable NNs with directed topology via ETI control. A kind of ETI controller is designed and Zeno behavior is avoided. Moreover, the multisynchronization of CNNs is applied to the associative memory for the first time. Compared with the multistability-based associative memory, the multisynchronization-based associative memory can have superiority in resisting the noise interference.