中国物理B ›› 2009, Vol. 18 ›› Issue (9): 3766-3771.doi: 10.1088/1674-1056/18/9/025

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Synchronization and parameter identification of one class of realistic chaotic circuit

王春妮, 马军, 褚润通, 李世荣   

  1. School of Science, Lanzhou University of Technology, Lanzhou 730050, China
  • 收稿日期:2009-03-01 修回日期:2009-04-14 出版日期:2009-09-20 发布日期:2009-09-20
  • 基金资助:
    Project partially supported by the National Nature Science Foundation of China (Grant No 10747005) and the Natural science foundation of Lanzhou University of Technology, China (Grant No Q200706).

Synchronization and parameter identification of one class of realistic chaotic circuit

Wang Chun-Ni(王春妮), Ma Jun(马军)†, Chu Run-Tong(褚润通), and Li Shi-Rong(李世荣)   

  1. School of Science, Lanzhou University of Technology, Lanzhou 730050, China
  • Received:2009-03-01 Revised:2009-04-14 Online:2009-09-20 Published:2009-09-20
  • Supported by:
    Project partially supported by the National Nature Science Foundation of China (Grant No 10747005) and the Natural science foundation of Lanzhou University of Technology, China (Grant No Q200706).

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摘要： In this paper, the synchronization and the parameter identification of the chaotic Pikovsky--Rabinovich (PR) circuits are investigated. The linear error of the second corresponding variables is used to change the driven chaotic PR circuit, and the complete synchronization of the two identical chaotic PR circuits is realized with feedback intensity k increasing to a certain threshold. The Lyapunov exponents of the chaotic PR circuits are calculated by using different feedback intensities and our results are confirmed. The case where the two chaotic PR circuits are not identical is also investigated. A general positive Lyapunov function V, which consists of all the errors of the corresponding variables and parameters and changeable gain coefficient, is constructed by using the Lyapunov stability theory to study the parameter identification and complete synchronization of two non-identical chaotic circuits. The controllers and the parameter observers could be obtained analytically only by simplifying the criterion dV/dt<0 (differential coefficient of Lyapunov function V with respect to time is negative). It is confirmed that the two non-identical chaotic PR circuits could still reach complete synchronization and all the unknown parameters in the drive system are estimated exactly within a short transient period.

Abstract: In this paper, the synchronization and the parameter identification of the chaotic Pikovsky--Rabinovich (PR) circuits are investigated. The linear error of the second corresponding variables is used to change the driven chaotic PR circuit, and the complete synchronization of the two identical chaotic PR circuits is realized with feedback intensity k increasing to a certain threshold. The Lyapunov exponents of the chaotic PR circuits are calculated by using different feedback intensities and our results are confirmed. The case where the two chaotic PR circuits are not identical is also investigated. A general positive Lyapunov function V, which consists of all the errors of the corresponding variables and parameters and changeable gain coefficient, is constructed by using the Lyapunov stability theory to study the parameter identification and complete synchronization of two non-identical chaotic circuits. The controllers and the parameter observers could be obtained analytically only by simplifying the criterion dV/dt<0 (differential coefficient of Lyapunov function V with respect to time is negative). It is confirmed that the two non-identical chaotic PR circuits could still reach complete synchronization and all the unknown parameters in the drive system are estimated exactly within a short transient period.

Key words: Pikovsky--Rabinovich, parameter identification, chaos, adaptive synchronization

中图分类号:  (Synchronization; coupled oscillators)

  • 05.45.Xt
02.30.Yy (Control theory) 05.45.Gg (Control of chaos, applications of chaos) 84.30.Bv (Circuit theory)