A novel mixed-synchronization phenomenon in coupled Chua's circuits via non-fragile linear control

doi:10.1088/1674-1056/20/8/080506

中国物理B ›› 2011, Vol. 20 ›› Issue (8): 80506-080506.doi: 10.1088/1674-1056/20/8/080506

A novel mixed-synchronization phenomenon in coupled Chua's circuits via non-fragile linear control

王军威, 马庆华, 曾丽

Cisco School of Informatics, Guangdong University of Foreign Studies, Guangzhou 510006, China

收稿日期:2011-02-08 修回日期:2011-04-23 出版日期:2011-08-15 发布日期:2011-08-15
基金资助:
Project supported by the Foundation for Distinguished Young Talents in Higher Education of Guangdong Province of China (Grant No. LYM10074) and the Natural Science Foundation of Guangdong Province, China (Grant No. 9451042001004076).

A novel mixed-synchronization phenomenon in coupled Chua's circuits via non-fragile linear control

Wang Jun-Wei(王军威)^†, Ma Qing-Hua(马庆华), and Zeng Li(曾丽)

Cisco School of Informatics, Guangdong University of Foreign Studies, Guangzhou 510006, China

Received:2011-02-08 Revised:2011-04-23 Online:2011-08-15 Published:2011-08-15
Supported by:
Project supported by the Foundation for Distinguished Young Talents in Higher Education of Guangdong Province of China (Grant No. LYM10074) and the Natural Science Foundation of Guangdong Province, China (Grant No. 9451042001004076).

摘要/Abstract

摘要： Dynamical variables of coupled nonlinear oscillators can exhibit different synchronization patterns depending on the designed coupling scheme. In this paper, a non-fragile linear feedback control strategy with multiplicative controller gain uncertainties is proposed for realizing the mixed-synchronization of Chua's circuits connected in a drive-response configuration. In particular, in the mixed-synchronization regime, different state variables of the response system can evolve into complete synchronization, anti-synchronization and even amplitude death simultaneously with the drive variables for an appropriate choice of scaling matrix. Using Lyapunov stability theory, we derive some sufficient criteria for achieving global mixed-synchronization. It is shown that the desired non-fragile state feedback controller can be constructed by solving a set of linear matrix inequalities (LMIs). Numerical simulations are also provided to demonstrate the effectiveness of the proposed control approach.

Abstract: Dynamical variables of coupled nonlinear oscillators can exhibit different synchronization patterns depending on the designed coupling scheme. In this paper, a non-fragile linear feedback control strategy with multiplicative controller gain uncertainties is proposed for realizing the mixed-synchronization of Chua's circuits connected in a drive-response configuration. In particular, in the mixed-synchronization regime, different state variables of the response system can evolve into complete synchronization, anti-synchronization and even amplitude death simultaneously with the drive variables for an appropriate choice of scaling matrix. Using Lyapunov stability theory, we derive some sufficient criteria for achieving global mixed-synchronization. It is shown that the desired non-fragile state feedback controller can be constructed by solving a set of linear matrix inequalities (LMIs). Numerical simulations are also provided to demonstrate the effectiveness of the proposed control approach.

Key words: mix-synchronization, Chua's circuit, non-fragile control, Lyapunov stability, linear matrix inequality

中图分类号: (Synchronization; coupled oscillators)

05.45.Xt

05.45.Gg (Control of chaos, applications of chaos) 05.45.-a (Nonlinear dynamics and chaos)

王军威, 马庆华, 曾丽. A novel mixed-synchronization phenomenon in coupled Chua's circuits via non-fragile linear control[J]. 中国物理B, 2011, 20(8): 80506-080506.

Wang Jun-Wei(王军威), Ma Qing-Hua(马庆华), and Zeng Li(曾丽) . A novel mixed-synchronization phenomenon in coupled Chua's circuits via non-fragile linear control[J]. Chin. Phys. B, 2011, 20(8): 80506-080506.

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A novel mixed-synchronization phenomenon in coupled Chua's circuits via non-fragile linear control

A novel mixed-synchronization phenomenon in coupled Chua's circuits via non-fragile linear control

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