5. Impulsive Synchronization of Chaotic Systems

In this paper, a new lemma is proposed to study the stability of a fractional order complex chaotic system without dividing the complex number into real and imaginary parts. The proving process of the new lemma combines the fundamental properties of the complex field and the fractional order extension of the Lyapunov direct method. It extends the fractional order extension of the Lyapunov direct method from the real number field to the complex number field. Based on the new lemma, we propose a new impulsive synchronization scheme for fractional order complex chaotic systems. The numerical simulation results also show the validity of our conclusion.

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Adaptive–impulsive synchronization and parameters estimation of chaotic systems with unknown parameters by using discontinuous drive signals

Applied Mathematical Modelling ◽

10.1016/j.apm.2014.12.028 ◽

2015 ◽

Vol 39 (14) ◽

pp. 3980-3989 ◽

Cited By ~ 14

Author(s):

Xiaojing Gao ◽

Hanping Hu

Keyword(s):

Chaotic Systems ◽

Parameters Estimation ◽

Unknown Parameters ◽

Impulsive Synchronization ◽

Drive Signals

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Impulsive Synchronization for T-S Fuzzy Model-based Chaotic Systems

2007 International Conference on Communications, Circuits and Systems ◽

10.1109/icccas.2007.4348242 ◽

2007 ◽

Cited By ~ 2

Author(s):

Qishui Zhong ◽

Yongbin Yu ◽

Jingfu Bao ◽

Songbai He

Keyword(s):

Chaotic Systems ◽

Fuzzy Model ◽

Impulsive Synchronization ◽

Model Based

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PRACTICAL STABILITY OF IMPULSIVE SYNCHRONIZATION BETWEEN TWO NONAUTONOMOUS CHAOTIC SYSTEMS

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127400000621 ◽

2000 ◽

Vol 10 (04) ◽

pp. 859-867 ◽

Cited By ~ 14

Author(s):

TAO YANG ◽

LEON O. CHUA

Keyword(s):

Differential Equation ◽

Impulsive Differential Equation ◽

Chaotic Systems ◽

Practical Stability ◽

Time Interval ◽

Theoretical Methods ◽

Synchronization Errors ◽

Impulsive Synchronization ◽

Error System ◽

Theoretical Results

The practical stability of impulsive synchronization between two nonautonomous chaotic systems is studied in this paper, and this is equivalent to that of the origin of the synchronization error system, which is modeled by an impulsive differential equation. We develop theoretical methods of choosing the time interval between two successive synchronization impulses and strengths of synchronization impulses for restricting synchronization errors within prescribed regions around the origin. Numerical experimental results are given to demonstrate theoretical results.

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