Function Projective Synchronization of Discrete-Time Chaotic and Hyperchaotic Systems Using Backstepping Method

2008 ◽  
Vol 50 (1) ◽  
pp. 111-116 ◽  
Author(s):  
Jin Yi-Liang ◽  
Li Xin ◽  
Chen Yong
Keyword(s):  
Discrete Time ◽  
Projective Synchronization ◽  
Backstepping Method ◽  
Function Projective Synchronization ◽  
Hyperchaotic Systems

FUNCTION PROJECTIVE SYNCHRONIZATION OF THE CHAOTIC SYSTEMS WITH PARAMETERS UNKNOWN

2013 ◽  
Vol 27 (21) ◽  
pp. 1350110
Author(s):  
JIAKUN ZHAO ◽  
YING WU
Keyword(s):  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Hyperchaotic System ◽  
Unknown Parameters ◽  
Function Projective Synchronization ◽  
Parameter Update Law ◽  
Different Chaotic Systems ◽  
Hyperchaotic Systems ◽  
Adaptive Control Law

This work is concerned with the general methods for the function projective synchronization (FPS) of chaotic (or hyperchaotic) systems. The aim is to investigate the FPS of different chaotic (hyper-chaotic) systems with unknown parameters. The adaptive control law and the parameter update law are derived to make the states of two different chaotic systems asymptotically synchronized up to a desired scaling function by Lyapunov stability theory. The general approach for FPS of Chen hyperchaotic system and Lü system is provided. Numerical simulations are also presented to verify the effectiveness of the proposed scheme.

Function Projective Synchronization of Discrete-Time Chaotic Systems

2008 ◽  
Vol 63 (1-2) ◽  
pp. 7-14 ◽  
Author(s):  
Xin Li ◽  
Yong Chen ◽  
Zhibin Li
Keyword(s):  
Discrete Time ◽  
Chaotic Systems ◽  
Scaling Function ◽  
Projective Synchronization ◽  
Discrete Time System ◽  
Time System ◽  
Function Projective Synchronization ◽  
Response Systems ◽  
Response State ◽  
Discrete Time Dynamical Systems

First, a function projective synchronization is defined in discrete-time dynamical systems, in which the drive and response state vectors evolve in a proportional scaling function matrix. Second, based on backstepping design with three controllers, a systematic, concrete and automatic scheme is developed to investigate the function projective synchronization of discrete-time chaotic systems. With the aid of symbolic-numeric computation, we use the proposed scheme to illustrate the function projective synchronization between the 2D Lorenz discrete-time system and the Fold discrete-time system, as well as between the 3D hyperchaotic Rössler discrete-time system and the Hénon-like map. Numeric simulations are used to verify the effectiveness of our scheme. By choosing different scaling functions, the interesting attractor figures of the drive and response systems are showed in a proportional scaling function.

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