Adaptive Control and Function Projective Synchronization in 2D Discrete-Time Chaotic Systems

2009 ◽  
Vol 51 (2) ◽  
pp. 270-278 ◽  
Author(s):  
Li Yin ◽  
Chen Yong ◽  
Li Biao
Keyword(s):  
Adaptive Control ◽  
Discrete Time ◽  
Chaotic Systems ◽  
Projective Synchronization ◽  
Function Projective Synchronization ◽  
And Function

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.

scholarly journals Universal Projective Synchronization of Two Different Hyperchaotic Systems with Unknown Parameters

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Baojie Zhang ◽  
Hongxing Li
Keyword(s):  
Adaptive Control ◽  
Chaotic Systems ◽  
Control Method ◽  
Scaling Function ◽  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Reference Systems ◽  
Unknown Parameters ◽  
Hyperchaotic Systems ◽  
Function Matrix

Universal projective synchronization (UPS) of two chaotic systems is defined. Based on the Lyapunov stability theory, an adaptive control method is derived such that UPS of two different hyperchaotic systems with unknown parameters is realized, which is up to a scaling function matrix and three kinds of reference systems, respectively. Numerical simulations are used to verify the effectiveness of the scheme.

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