Complete synchronization, phase synchronization and parameters estimation in a realistic chaotic system. (English) Zbl 1222.65136

Ma, Jun; Li, Fan; Huang, Long; Jin, Wu-Yin

Commun. Nonlinear Sci. Numer. Simul. 16, No. 9, 3770-3785 (2011).

Summary: The two-parameter phase space in certain nonlinear system is investigated and the chaotic region of parameters are measured to show its chaotic properties. Within the chaotic parameter region, the complete synchronization, phase synchronization and parameters estimation are discussed in detail by using adaptive synchronization scheme and Lyapunov stability theory. Two changeable gain coefficients are introduced into the controllable positive Lyapunov function and thus the parameter observers. It is found that complete synchronization or phase synchronization occurs with different controllers being used though the parameter observers are the same. Phase synchronization is observed when a zero eigenvalue of the Jacobi matrix, which is composed of the errors of corresponding variables in the drive and driven chaotic systems. The optimized selection of controllers can induce transition of phase synchronization and complete synchronization.

MSC:

65P20	Numerical chaos
93B05	Controllability
93D05	Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
93C15	Control/observation systems governed by ordinary differential equations
37D45	Strange attractors, chaotic dynamics of systems with hyperbolic behavior

Keywords:

phase synchronization; complete synchronization; Jacobi matrix; parameter estimation; numerical examples; chaotic parameter region; Lyapunov stability; controllers; chaotic systems

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