The Synchronisation Problem of Chaotic Neural Networks Based on Saturation Impulsive Control and Intermittent Control

Abstract

This paper primarily focuses on the chaos synchronisation analysis of neural networks (NNs) under a hybrid controller. Firstly, we design a suitable hybrid controller with saturated impulse control, combined with time-dependent intermittent control. Both controls are low-energy consumption and discrete, aligning well with industrial development needs. Secondly, the saturation function in the chaotic neural network is addressed using the polyhedral representation method and the sector nonlinearity method, respectively. By integrating the Lyapunov stability theory, Jensen’s inequality, the mathematical induction method, and the inequality reduction technique, we establish suitable time-dependent Lyapunov generalised equations. This leads to the estimation of the domain of attraction and the derivation of local exponential stability conditions for the error system. The validity of the achieved theoretical criteria is eventually demonstrated through numerical experiment simulations.

A Novel Chaotic System with Only Quadratic Nonlinearities: Analysis of Dynamical Properties and Stability

“…Furthermore, alongside these explorations into new and adapted chaotic systems, a parallel line of investigation has emerged delving into strategies for controlling chaos in nonlinear dynamics. On the other hand, certain investigations have pursued strategies for controlling nonlinear dynamics, such as controlling chaos synchronization [31] or special dynamical properties [32].…”