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Chaos synchronization of two different chaotic complex Chen and Lü systems. (English) Zbl 1170.70011

Summary: This paper investigates the chaos synchronization of two different chaotic complex systems of the Chen and Lü type [S. Chen and J. Lü, Chaos Solitons Fractals 14, No. 4, 643–647 (2002; Zbl 1005.93020)] via the methods of active control and global synchronization. In this regard, it generalizes earlier work on the synchronization of two identical oscillators in the cases where the drive and response systems are different, the parameter space is larger, and the dimensionality increases due to the complexification of dependent variables. The idea of chaos synchronization is to use the output of the drive system to control the response system, so that the output of the response system converges to the output of the drive system as time increases. Lyapunov functions are derived to prove that the differences in the dynamics of the two systems converge to zero exponentially fast, explicit expressions are given for the control functions, and numerical simulations are presented to illustrate our chaos synchronization techniques. We also point out that the global synchronization method is better suited for synchronizing identical chaotic oscillators, as it has serious limitations when applied to the case where the drive and response systems are different.

MSC:

70K55 Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics
70Q05 Control of mechanical systems

Citations:

Zbl 1005.93020
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References:

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