Function projective synchronization of Liu system and the new Lorenz system with known and unknown parameters

2012 ◽  
Author(s):  
Xuan Li ◽  
Wuneng Zhou ◽  
Siming Ma ◽  
Shicao Luo ◽  
Rui Chen
Keyword(s):  
Lorenz System ◽  
Projective Synchronization ◽  
Unknown Parameters ◽  
Function Projective Synchronization ◽  
Liu System

Adaptive Hybrid Function Projective Synchronization of General Chaotic Complex Systems With Different Orders

2015 ◽  
Vol 10 (2) ◽  
Author(s):  
Ping Liu
Keyword(s):  
Nonlinear Systems ◽  
Complex Systems ◽  
Lorenz System ◽  
Mathematical Expression ◽  
Projective Synchronization ◽  
Unknown Parameters ◽  
Chen System ◽  
Function Projective Synchronization ◽  
Hybrid Function ◽  
Complex Lorenz System

A lot of progress has been made in the research of hybrid function projective synchronization (HFPS) for chaotic real nonlinear systems, while the HFPS of two different chaotic complex nonlinear systems with nonidentical dimensions is seldom reported in the literatures. So this paper discusses the HFPS of general chaotic complex system described by a unified mathematical expression with different dimensions and fully unknown parameters. Based on the Lyapunov stability theory, the adaptive controller is designed to synchronize two general uncertain chaotic complex systems with different orders in the sense of HFPS and the parameter update laws for estimating unknown parameters of chaotic complex systems are also given. Moreover, the control coefficients can be automatically adapted to updated laws. Finally, the HFPS between hyperchaotic complex Lorenz system and complex Chen system and that between chaotic complex Lorenz system and hyperchaotic complex Lü are taken as two examples to demonstrate the effectiveness and feasibility of the proposed HFPS 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.

Generalized Projective Synchronization of Diverse Structures Hyperchaotic Systems with Unknown Parameters

2014 ◽  
Vol 568-570 ◽  
pp. 1095-1099
Author(s):  
Si Yan Tao ◽  
Da Lin ◽  
Xiao Hui Zeng
Keyword(s):  
General Class ◽  
Lorenz System ◽  
Projective Synchronization ◽  
Unknown Parameters ◽  
Chen System ◽  
Control Approach ◽  
Response System ◽  
Hyperchaotic Lorenz System ◽  
Generalized Projective Synchronization ◽  
Hyperchaotic Systems

In this paper, the generalized projective synchronization for a general class of hyperchaotic systems is investigated. A systematic, powerful and concrete scheme is developed to investigate the generalized projective synchronization between the drive system and response system based on the feedback control approach. The hyperchaotic Chen system and hyperchaotic Lorenz system are chosen to illustrate the proposed scheme. Numerical simulations are provided to show the effectiveness of the proposed schemes.

GENERALIZED (LAG, ANTICIPATED AND COMPLETE) PROJECTIVE SYNCHRONIZATION IN TWO NONIDENTICAL CHAOTIC SYSTEMS WITH UNKNOWN PARAMETERS

2012 ◽  
Vol 26 (16) ◽  
pp. 1250121
Author(s):  
XINGYUAN WANG ◽  
LULU WANG ◽  
DA LIN
Keyword(s):  
Adaptive Control ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Control Method ◽  
Projective Synchronization ◽  
Unknown Parameters ◽  
Chen System ◽  
Control Approach ◽  
Response System ◽  
Hyperchaotic Lorenz System

In this paper, a generalized (lag, anticipated and complete) projective synchronization for a general class of chaotic systems is defined. A systematic, powerful and concrete scheme is developed to investigate the generalized (lag, anticipated and complete) projective synchronization between the drive system and response system based on the adaptive control method and feedback control approach. The hyperchaotic Chen system and hyperchaotic Lorenz system are chosen to illustrate the proposed scheme. Numerical simulations are provided to show the effectiveness of the proposed schemes. In addition, the scheme can also be extended to research generalized (lag, anticipated and complete) projective synchronization between nonidentical discrete-time chaotic systems.

Complete Switched Generalized Function Projective Synchronization of a Class of Hyperchaotic Systems With Unknown Parameters and Disturbance Inputs

2013 ◽  
Vol 136 (1) ◽  
Author(s):  
Fei Yu ◽  
Yun Song
Keyword(s):  
Numerical Simulations ◽  
Scaling Function ◽  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Generalized Function ◽  
Unknown Parameters ◽  
Function Projective Synchronization ◽  
Parameter Update Law ◽  
Hyperchaotic Systems ◽  
Generalized Function Projective Synchronization

The concept of complete switched generalized function projective synchronization (CSGFPS) in practical type is introduced and the CSGFPS of a class of hyperchaotic systems with unknown parameters and disturbance inputs are investigated. By Lyapunov stability theory, the adaptive control law and the parameter update law are derived to make the states of a class of hyperchaotic systems asymptotically synchronized up to a desired scaling function and the unknown parameters are also estimated. In numerical simulations, the scaling function factors discussed in this paper are more complicated. Finally, the hyperchaotic Lorenz and hyperchaotic Lü systems are taken, for example, and the numerical simulations are presented to verify the effectiveness and robustness of the proposed control scheme.

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