The Generalized Dahlquist Constant with Applications in Synchronization Analysis of Typical Neural Networks via General Intermittent Control

Abstract

A novel and effective approach to synchronization analysis of neural networks is investigated by using the nonlinear operator named the generalized Dahlquist constant and the general intermittent control. The proposed approach offers a design procedure for synchronization of a large class of neural networks. The numerical simulations whose theoretical results are applied to typical neural networks with and without delayed item demonstrate the effectiveness and feasibility of the proposed technique.

A Class of Vector Lyapunov Functions for Stability Analysis of Nonlinear Impulsive Differential Systems

“…Definition 1 (see [12,14,15,19]). System (1) is called to be exponentially stable on a neighborhood Ω of the equilibrium point, if there exist constants > 0, > 0 such that…”

“…There has been a significant development in the theory of the impulsive differential systems within the past 20 years (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]). The efficient applications of impulsive differential systems require the finding of criteria for stability of their solutions.…”

Synchronization of Multi-Chaotic Systems with Ring and Chain Intermittent Connections

“…Since Pecora and Carrol introduced the concept of synchronization and made it a reality in electronic circuits in 1990 [1] , synchronization of chaotic systems is of great practical significance and has received great interest in recent years [2][3][4][5][6] . Many methods for chaos synchronization have appeared in the last few years, such as driver-response synchronization, active control, adaptive synchronization, variable feedback approach, and so on [1][2][3][4][5][6][7][8][9][10][11][12] . As we all known, the above methods are all to construct proper Lyapunov functions which are usually very skillful.…”

“…Intermittent control [13][14][15][16][17] has been used for a variety of purposes in engineering fields such as manufacturing, transportation,air-quality control, and communication. Synchronization using an intermittent control method has been discussed in [10,[14][15][16][17]. Compared with continuous control methods [1][2][3][4][5][6][7][8][9][10][11][12] , intermittent control is more efficient when the system output is measured intermittently rather than continuously.…”

“…Synchronization using an intermittent control method has been discussed in [10,[14][15][16][17]. Compared with continuous control methods [1][2][3][4][5][6][7][8][9][10][11][12] , intermittent control is more efficient when the system output is measured intermittently rather than continuously. Our interest focuses on the class of intermittent control with time duration, wherein the control is activated in certain nonzero time intervals, and is off in other time intervals.…”