Generalized synchronization of different orders of chaotic systems with unknown parameters and parameter identification

Abstract

Using add-order method to translate the problem of generalized synchronization of different orders of chaotic systems into the synchronization of systems of identical order. Based on Lyapunov stability theory and adaptive control method, we give the expression of adaptive controller and the updating rule of parameters, then achieve generalized synchronization of different order of chaotic systems with unknown parameters and enable the estimation of the parameters of the drive and the response systems. This method has been applied to solve the generalized synchronization problem of hyperchaotic Lü system, Lorenz system, generalized Lorenz system, and Liu system with unknown parameters. It is proved theoretically that this method is feasible. Numerical simulations show the effectiveness of the adaptive control technique.

General hybrid projective complete dislocated synchronization with non-derivative and derivative coupling based on parameter identification in several chaotic and hyperchaotic systems

“…So far, several theoretical methods have been developed to realize chaos synchronization, such as the feedback control method, [3][4][5][6] the adaptive control method, [7][8][9] the active-control control method, [10] the impulsive control method, [11] the passive control method, [12] the Bang-Bang control method, [13] and the robust control method, [14] etc. Up until now, different kinds of synchronization have been intensively studied and many theoretical results have been obtained, including generalized synchronization, [15][16][17] complete synchronization, [18] partial synchronization, [19] phase synchronization, [20,21] anti-phase synchronization, [22,23] lag synchronization, [24,25] and projective synchronization. [26][27][28][29] Hu et al [30] considered a full state hybrid projective synchronization (FSHPS), which bridges the gap from chaos con-trol to chaos synchronization in some literature.…”

Generalized projective synchronization of chaotic systems via adaptive learning control

“…Since the idea of synchronising two identical autonomous chaotic systems under different initial conditions was first introduced in 1990 by Pecora and Carroll, [1] chaos synchronisation has been widely studied in physics, secure communication, chemical reactor, biological networks and artificial neural networks. Up to now, different types of synchronisation phenomena have been presented such as complete synchronisation (CS), [2] generalized synchronisation, [3] phase synchronisation, [4] etc. Besides many control schemes such as the OGY method, [5] delayed feedback method, [6] state observer approach, [7] adaptive control method, [8] and active control [9] approach have been employed to synchronize chaotic systems with different initial conditions.…”

Projective Synchronization of Complex Dynamical Networks with Time-Varying Coupling Strength via Hybrid Feedback Control

“…One of the most remarkable phenomena in the dynamics of networks is their spontaneous synchronization, which has been carefully studied in recent years. [5−9] Up to now, different types of synchronization phenomena have been presented, such as complete synchronization, [10] generalized synchronization, [11] phase synchronization, [12] projective synchronization, [13] etc. In addition, many control schemes such as the delayed feedback method, [14] the state observer approach, [15] the adaptive control method [16] and the active control [17] approach have been employed to synchronize complex dynamical networks with different initial conditions.…”