Master-Slave Synchronization of Chaotic Φ6 Duffing Oscillators by Linear State Error Feedback Control

Ke Ding

doi:10.1155/2019/3637902

Abstract

This paper is concerned with master-slave synchronization of chaotic Φ6 Duffing oscillators by using linear state error feedback control. Compared with some existing methods and results, this paper estimates the bound of the first trajectory (variable) of the controlled slave system and uses this bound to derive synchronization criteria for two chaotic Φ6 Duffing oscillators. The effectiveness of synchronization criteria is illustrated by three simulation examples.

Highlights

Synchronization of chaotic systems has received considerable attention due to its theoretical importance and practical applications in secure communication and signal processing.As is well known, some models for damped and driven oscillators, such as sti ening springs, beam bulking, and superconducting Josephson parametric ampli ers, can be described as Φ6 Du ng oscillators which have been widely used in mechanical and electrical systems [1, 9,10,11, 32,33,34,35,36]
For chaotic Φ6 Du ng oscillators, Njah [10, 11] used the active control to achieve master-slave synchronization, in which the active control removed all nonlinear terms of the error system
For chaotic Φ4 Du ng oscillators which is the special case of Φ6 Du ng oscillators, synchronization criteria were derived by the active control in [32,33,34, 37] and [35] in which the linear error system and synchronization criteria were derived

Summary

Introduction

Synchronization of chaotic systems has received considerable attention due to its theoretical importance and practical applications in secure communication and signal processing (see for example, [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31] and references therein). Us, how to use the nonlinear properties of the error system and how to use linear state error feedback control to derive synchronization criteria for chaotic Φ6 Du ng oscillators is one motivation of this paper. E bounds of trajectories of the master system and slave system have been widely used to derive the synchronization criteria for chaotic systems (see for example, [36, 38,39,40]). Erefore, how to derive the bound of some (not all) trajectories of the controlled slave system before the master system and the slave system achieve synchronization and how to use the derived bound to achieve synchronization criteria for the chaotic Φ6 Du ng oscillators is another motivation of this paper. We will construct a master-slave synchronization scheme for chaotic Φ6 Du ng oscillators by using linear state error feedback control. E purpose of this paper is to investigate the masterslave synchronization for the system described by (1) and to find the controller gain K, such that the system described by (10) is globally asymptotically stable, which indicates that the system described by (7)–(9) synchronizes

Main Results

Master-Slave Synchronization of Classic Φ4 Duffing

Simulation Study

Conclusion