5. Impulsive Synchronization of Chaotic Systems

2005 ◽  
pp. 107-126
Author(s):  
Zhengguo Li ◽  
Yengchai Soh ◽  
Changyun Wen
Keyword(s):  
Chaotic Systems ◽  
Impulsive Synchronization

A new contribution for the impulsive synchronization of fractional-order discrete-time chaotic systems

2017 ◽  
Vol 90 (3) ◽  
pp. 1519-1533 ◽  
Author(s):  
Ouerdia Megherbi ◽  
Hamid Hamiche ◽  
Saïd Djennoune ◽  
Maamar Bettayeb
Keyword(s):  
Fractional Order ◽  
Discrete Time ◽  
Chaotic Systems ◽  
Impulsive Synchronization

Adaptive impulsive synchronization for a class of fractional order complex chaotic systems

2019 ◽  
Vol 25 (10) ◽  
pp. 1614-1628 ◽  
Author(s):  
Xingpeng Zhang ◽  
Dong Li ◽  
Xiaohong Zhang
Keyword(s):  
Number Field ◽  
Fractional Order ◽  
Complex Number ◽  
Chaotic Systems ◽  
Direct Method ◽  
Order Complex ◽  
Lyapunov Direct Method ◽  
Impulsive Synchronization ◽  
Complex Chaotic Systems ◽  
Order Extension

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.

PRACTICAL STABILITY OF IMPULSIVE SYNCHRONIZATION BETWEEN TWO NONAUTONOMOUS CHAOTIC SYSTEMS

2000 ◽  
Vol 10 (04) ◽  
pp. 859-867 ◽  
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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