scholarly journals A Novel Hybrid Function Projective Synchronization between Different Fractional-Order Chaotic Systems

2011 ◽  
Vol 2011 ◽  
pp. 1-15
Author(s):  
Ping Zhou ◽  
Xiao-You Yang
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Scaling Function ◽  
Uncertain System ◽  
Adaptive Controller ◽  
Projective Synchronization ◽  
Function Projective Synchronization ◽  
Response System ◽  
Parameter Update Law ◽  
Hybrid Function

An adaptive hybrid function projective synchronization (AHFPS) scheme between different fractional-order chaotic systems with uncertain system parameter is addressed in this paper. In this proposed scheme, the drive and response system could be synchronized up to a vector function factor. This proposed scheme is different with the function projective synchronization (FPS) scheme, in which the drive and response system could be synchronized up to a scaling function factor. The adaptive controller and the parameter update law are gained. Two examples are presented to demonstrate the effectiveness of the proposed scheme.

THE HYBRID FUNCTION PROJECTIVE SYNCHRONIZATION OF CHAOTIC SYSTEMS

2009 ◽  
Vol 20 (05) ◽  
pp. 789-797
Author(s):  
YONG-GUANG YU ◽  
HAN-XIONG LI ◽  
JUN-ZHI YU
Keyword(s):  
Numerical Simulation ◽  
Lyapunov Stability ◽  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
Adaptive Controller ◽  
Projective Synchronization ◽  
Function Projective Synchronization ◽  
Hybrid Function ◽  
Simulation Results ◽  
Different Chaotic Systems

This paper mainly investigated a hybrid function projective synchronization of two different chaotic systems. Based on the Lyapunov stability theory, an adaptive controller for the synchronization of two different chaotic systems is designed. This technique is applied to achieve the synchronization between Lorenz and Rössler chaotic systems, and the synchronization of hyperchaotic Rössler and Chen systems. The numerical simulation results illustrate the effectiveness and feasibility of the proposed scheme.

Fuzzy Adaptive Controller for Synchronization of Uncertain Fractional-Order Chaotic Systems

2018 ◽  
pp. 190-217 ◽  
Author(s):  
Amel Bouzeriba
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Adaptive Controller ◽  
Projective Synchronization ◽  
External Disturbances ◽  
Fuzzy Approximation ◽  
Adaptive Laws ◽  
Adaptive Fuzzy Logic ◽  
Fuzzy Adaptive Controller ◽  
Fuzzy Adaptive

In this chapter, the projective synchronization problem of different multivariable fractional-order chaotic systems with both uncertain dynamics and external disturbances is studied. More specifically, a fuzzy adaptive controller is investigated for achieving a projective synchronization of uncertain fractional-order chaotic systems. The adaptive fuzzy-logic system is used to online estimate the uncertain nonlinear functions. The latter is augmented by a robust control term to efficiently compensate for the unavoidable fuzzy approximation errors, external disturbances as well as residual error due to the use of the so-called e-modification in the adaptive laws. A Lyapunov approach is employed to derive the parameter adaptation laws and to prove the boundedness of all signals of the closed-loop system. Numerical simulations are performed to verify the effectiveness of the proposed synchronization scheme.

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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