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.
Received: 01 March 2009
Revised: 14 April 2009
Accepted manuscript online:
Fund: 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).
Cite this article:
Wang Chun-Ni(王春妮), Ma Jun(马军), Chu Run-Tong(褚润通), and Li Shi-Rong(李世荣) Synchronization and parameter identification of one class of realistic chaotic circuit 2009 Chin. Phys. B 18 3766
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