Dynamical and Static Multisynchronization of Coupled Multistable Neural Networks via Impulsive Control

Abstract

This paper investigates the dynamical multisynchronization and static multisynchronization problem for delayed coupled multistable neural networks with fixed and switching topologies. To begin with, a class of activation functions as well as several sufficient conditions are introduced to ensure that every subnetwork has multiple equilibrium states. By constructing an appropriate Lyapunov function and by employing impulsive control theory and the average impulsive interval method, several sufficient conditions for multisynchronization in terms of linear matrix inequalities (LMIs) are obtained. Moreover, a unified impulsive controller is designed by means of the established LMIs. Finally, a numerical example is presented to demonstrate the effectiveness of the presented impulsive control strategy.

Hybrid multisynchronization of coupled multistable memristive neural networks with time delays

“…In literatures [15,16,17,18,19,20], [26,27,28,29,30,31], [45,46], synchronization was addressed under a stable equilibrium state. As discussed previously, multiple stable equilibrium states are very necessary for coupled systems including CMMNNs in some applications [12,13,14], [23,24], [32,33,34], [36,37,38,39,40,41,42]. Therefore, when coupled systems have multiple stable equilibrium states, how to achieve synchro- [32].…”

“…Compared with an isolated system, coupled systems have wider applications in many fields [23,24,25], such as robots, dynamic image processing, associative memory of video. Therefore, some dynamic characteristics of coupled systems were investigated in recent years [25,26,27,28,29,30,31,32,33,34,35,36]. For example, synchronization of coupled NN systems was researched in [30,31] and [35].…”

“…In [32,33,34], multistability and multisynchronization of coupled multistable NN systems were investigated. However, there is no relevant work on studying dynamic characteristics of coupled multistable MNN (CMMNN) systems.…”

“…In the above researches [13,14], MNNs can only obtain a small quantity of stable e-quilibrium states with a few corner points. Actually, as many stable equilibrium states as possible are very necessary for coupled systems including CMMNNs in some applications [12,13,14], [23,24], [32,33,34], [36,37,38,39,40,41,42], such as associative memory storage, image processing.…”

“…And synchronization has broad potential applications in many areas [25], [44], such as secure communication, biological systems and so on. Over the years, there are many researches on studying synchronization problems [15,16,17,18,19,20], [26,27,28,29,30,31,32,33,34,35], [45,46]. For example, exponential synchronization of inertial BAM NNs [45], MNNs [15] and coupled MNNs [26] was researched.…”