Synchronization and parameter identification of one class of realistic chaotic circuit

In this paper, the synchronization and the parameter identificationof the chaotic Pikovsky--Rabinovich (PR) circuits are investigated.The linear error of the second corresponding variables is used tochange the driven chaotic PR circuit, and the completesynchronization of the two identical chaotic PR circuits is realizedwith feedback intensity k increasing to a certain threshold. TheLyapunov exponents of the chaotic PR circuits are calculated byusing different feedback intensities and our results are confirmed.The case where the two chaotic PR circuits are not identical is alsoinvestigated. A general positive Lyapunov function V, whichconsists of all the errors of the corresponding variables andparameters and changeable gain coefficient, is constructed by usingthe Lyapunov stability theory to study the parameter identificationand complete synchronization of two non-identical chaotic circuits.The controllers and the parameter observers could be obtainedanalytically only by simplifying the criterion dV/dt<0(differential coefficient of Lyapunov function V with respect totime is negative). It is confirmed that the two non-identicalchaotic PR circuits could still reach complete synchronization andall the unknown parameters in the drive system are estimated exactlywithin a short transient period.