Adaptive Synchronization Between Hyperchaotic Lorenz System and Chen System

2009 ◽  
Author(s):  
Francis Austin ◽  
Chen Xu ◽  
Jian-wen Feng ◽  
Wei-qiang Zhang
Keyword(s):  
Lorenz System ◽  
Adaptive Synchronization ◽  
Chen System ◽  
Hyperchaotic Lorenz System

scholarly journals Inverse Projective Synchronization between Two Different Hyperchaotic Systems with Fractional Order

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Yi Chai ◽  
Liping Chen ◽  
Ranchao Wu
Keyword(s):  
Fractional Order ◽  
Lorenz System ◽  
Projective Synchronization ◽  
Generalized Synchronization ◽  
Fractional Order Systems ◽  
Chen System ◽  
Fractional Order Differential Equations ◽  
Hyperchaotic Lorenz System ◽  
The Stability ◽  
Hyperchaotic Systems

This paper mainly investigates a novel inverse projective synchronization between two different fractional-order hyperchaotic systems, that is, the fractional-order hyperchaotic Lorenz system and the fractional-order hyperchaotic Chen system. By using the stability theory of fractional-order differential equations and Lyapunov equations for fractional-order systems, two kinds of suitable controllers for achieving inverse projective synchronization are designed, in which the generalized synchronization, antisynchronization, and projective synchronization of fractional-order hyperchaotic Lorenz system and fractional-order hyperchaotic Chen system are also successfully achieved, respectively. Finally, simulations are presented to demonstrate the validity and feasibility of the proposed method.

GENERALIZED SYNCHRONIZATION OF NONIDENTICAL FRACTIONAL-ORDER CHAOTIC SYSTEMS

2013 ◽  
Vol 27 (30) ◽  
pp. 1350195 ◽  
Author(s):  
XING-YUAN WANG ◽  
ZUN-WEN HU ◽  
CHAO LUO
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Pole Placement ◽  
Generalized Synchronization ◽  
Chen System ◽  
Hyperchaotic Lorenz System ◽  
The Stability ◽  
Synchronization Scheme ◽  
Placement Technique

In this paper, a chaotic synchronization scheme is proposed to achieve the generalized synchronization between two different fractional-order chaotic systems. Based on the stability theory of fractional-order systems and the pole placement technique, a controller is designed and theoretical proof is given. Two groups of examples are shown to verify the effectiveness of the proposed scheme, the first one is to realize the generalized synchronization between the fractional-order Chen system and the fractional-order Rössler system, the second one is between the fractional-order Lü system and the fractional-order hyperchaotic Lorenz system. The corresponding numerical simulations 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.

scholarly journals Synchronization of Coupled Nonidentical Fractional-Order Hyperchaotic Systems

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
Zhouchao Wei
Keyword(s):  
Fractional Order ◽  
Lorenz System ◽  
Sliding Mode ◽  
Sliding Mode Controller ◽  
Control Parameters ◽  
Chen System ◽  
Mode Method ◽  
Hyperchaotic Lorenz System ◽  
Hyperchaotic Systems

Synchronization of coupled nonidentical fractional-order hyperchaotic systems is addressed by the active sliding mode method. By designing an active sliding mode controller and choosing proper control parameters, the master and slave systems are synchronized. Furthermore, synchronizing fractional-order hyperchaotic Lorenz system and fractional-order hyperchaotic Chen system is performed to show the effectiveness of the proposed controller.

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.

BRIDGE BETWEEN THE HYPERCHAOTIC LORENZ SYSTEM AND THE HYPERCHAOTIC CHEN SYSTEM

2011 ◽  
Vol 25 (05) ◽  
pp. 711-721 ◽  
Author(s):  
CHAO MA ◽  
XINGYUAN WANG
Keyword(s):  
Bifurcation Analysis ◽  
System Parameter ◽  
Lorenz System ◽  
Hyperchaotic System ◽  
Lyapunov Dimension ◽  
Dual Systems ◽  
Chen System ◽  
New Findings ◽  
Hyperchaotic Lorenz System ◽  
New System

This paper presents a novel unified hyperchaotic system that contains the hyperchaotic Lorenz system and the hyperchaotic Chen system as two dual systems at the two extremes of its parameter spectrum. The new system is hyperchaotic over almost the whole range of the system parameter and continuously transfers from the hyperchaotic Lorenz system to the hyperchaotic Chen system. The new findings are not only demonstrated by computer simulations but also verified with bifurcation analysis, Lyapunov exponents and Lyapunov dimension.

ADAPTIVE GENERALIZED SYNCHRONIZATION OF HYPERCHAOS SYSTEMS

2011 ◽  
Vol 25 (32) ◽  
pp. 4563-4571 ◽  
Author(s):  
XINGYUAN WANG ◽  
YAQIN WANG
Keyword(s):  
Chaotic Systems ◽  
Lorenz System ◽  
Lyapunov Stability Theory ◽  
New Method ◽  
Generalized Synchronization ◽  
Chen System ◽  
Response Systems ◽  
Hyperchaotic Lorenz System ◽  
Linear And Nonlinear ◽  
Simulation Results

This paper studies the generalized synchronization of hyperchaos systems, and a new method, by which adaptive generalized synchronization of chaotic systems with a kind of linear and nonlinear relationship between the drive and response systems can be achieved, is proposed. This new method has more extensive application scope. Based on the Lyapunov stability theory, the correctness of the proposed scheme is strictly demonstrated. It is also illustrated by applications to hyperchaotic Chen system and hyperchaotic Lorenz system and the simulation results show the effectiveness of the proposed scheme.

Dynamics, Synchronization and Electronic Implementations of a New Lorenz-like Chaotic System with Nonhyperbolic Equilibria

2019 ◽  
Vol 29 (14) ◽  
pp. 1950197 ◽  
Author(s):  
P. D. Kamdem Kuate ◽  
Qiang Lai ◽  
Hilaire Fotsin
Keyword(s):  
Chaotic System ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Chaotic Behavior ◽  
Piecewise Linear ◽  
Period Doubling ◽  
Adaptive Synchronization ◽  
The Novel ◽  
Algebraic Equations ◽  
The Lorenz System

The Lorenz system has attracted increasing attention on the issue of its simplification in order to produce the simplest three-dimensional chaotic systems suitable for secure information processing. Meanwhile, Sprott’s work on elegant chaos has revealed a set of 19 chaotic systems all described by simple algebraic equations. This paper presents a new piecewise-linear chaotic system emerging from the simplification of the Lorenz system combined with the elegance of Sprott systems. Unlike the majority, the new system is a non-Shilnikov chaotic system with two nonhyperbolic equilibria. It is multiplier-free, variable-boostable and exclusively based on absolute value and signum nonlinearities. The use of familiar tools such as Lyapunov exponents spectra, bifurcation diagrams, frequency power spectra as well as Poincaré map help to demonstrate its chaotic behavior. The novel system exhibits inverse period doubling bifurcations and multistability. It has only five terms, one bifurcation parameter and a total amplitude controller. These features allow a simple and low cost electronic implementation. The adaptive synchronization of the novel system is investigated and the corresponding electronic circuit is presented to confirm its feasibility.

Sign in / Sign up

Export Citation Format

Share Document