scholarly journals Chaos in the fractional-order conjugate Chen system and its circuit emulation

2009 ◽  
Vol 58 (5) ◽  
pp. 2957
Author(s):  
Zhang Ruo-Xun ◽  
Yang Shi-Ping
Keyword(s):  
Fractional Order ◽  
Chen System

scholarly journals Adaptive Projective Synchronization between Two Different Fractional-Order Chaotic Systems with Fully Unknown Parameters

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Liping Chen ◽  
Shanbi Wei ◽  
Yi Chai ◽  
Ranchao Wu
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Projective Synchronization ◽  
Control Law ◽  
Unknown Parameters ◽  
Chen System ◽  
Fractional Order Differential Equations ◽  
Response Systems ◽  
The Stability ◽  
Adaptive Control Law

Projective synchronization between two different fractional-order chaotic systems with fully unknown parameters for drive and response systems is investigated. On the basis of the stability theory of fractional-order differential equations, a suitable and effective adaptive control law and a parameter update rule for unknown parameters are designed, such that projective synchronization between the fractional-order chaotic Chen system and the fractional-order chaotic Lü system with unknown parameters is achieved. Theoretical analysis and numerical simulations are presented to demonstrate the validity and feasibility of the proposed method.

Emulating “Chaos + Chaos = Order” in Chen’s Circuit of Fractional Order by Parameter Switching

2016 ◽  
Vol 26 (06) ◽  
pp. 1650096 ◽  
Author(s):  
Wallace K. S. Tang ◽  
Marius-F. Danca
Keyword(s):  
Fractional Order ◽  
Electronic Circuit ◽  
Chaotic Circuit ◽  
Chen System ◽  
Potential Applications ◽  
Simulation And Experiment ◽  
Averaged Model ◽  
First Time ◽  
Important Design ◽  
Parameter Switching

In this paper, the effect of the parameter switching (PS) algorithm in a fractional order chaotic circuit is investigated both in simulation and experiment. The Chen system of fractional order is focused and realized in an electronic circuit. By designing a switching circuit, the PS algorithm is implemented and it is the first time, the paradoxical “Chaos [Formula: see text] Chaos [Formula: see text] Order” is presented in an electronic circuit. Both the simulation and experimental results confirm that the obtained attractor under switching approximates the attractor of the time-averaged model. Some important design issues for the circuitry realization of the PS scheme are pointed out. Finally, our work confirms the practical usage of PS algorithm in potential applications such as attractor synthesis and chaos control.

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.

CHAOS GENERATED FROM THE FRACTIONAL-ORDER COMPLEX CHEN SYSTEM AND ITS APPLICATION TO DIGITAL SECURE COMMUNICATION

2013 ◽  
Vol 24 (04) ◽  
pp. 1350025 ◽  
Author(s):  
CHAO LUO ◽  
XINGYUAN WANG
Keyword(s):  
Fractional Order ◽  
Secure Communication ◽  
High Capacity ◽  
Projective Synchronization ◽  
Largest Lyapunov Exponent ◽  
Order Complex ◽  
State Variables ◽  
Chen System ◽  
Time Dynamic ◽  
Irregular Pattern

In this paper, a novel dynamic system, the fractional-order complex Chen system, is presented for the first time. Dynamic behaviors of system are studied analytically and numerically. Different routes to chaos are shown, and diverse kinds of motions are identified and exhibited by means of bifurcation diagram, portrait phase and the largest Lyapunov exponent. Secondly, an application to digital secure communication based on the novel system is proposed, in which security is enhanced by continually switching different orders of derivative in an irregular pattern. Furthermore, making full use of the advantage of high-capacity transmission of complex system, the improved digital secure communication scheme is achieved based on hybrid synchronization in coupled fractional-order complex Chen system, that means anti-synchronization in real part of state variables and projective synchronization in imaginary part, respectively. The corresponding numerical simulations demonstrate the effectiveness and feasibility of the proposed schemes.

scholarly journals Synchronization between Fractional-Order and Integer-Order Hyperchaotic Systems via Sliding Mode Controller

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Yan-Ping Wu ◽  
Guo-Dong Wang
Keyword(s):  
Theoretical Analysis ◽  
Fractional Order ◽  
Chaotic System ◽  
Sliding Mode ◽  
Sliding Mode Controller ◽  
Control Parameters ◽  
Chen System ◽  
Integer Order ◽  
Response Systems ◽  
Hyperchaotic Systems

The synchronization between fractional-order hyperchaotic systems and integer-order hyperchaotic systems via sliding mode controller is investigated. By designing an active sliding mode controller and choosing proper control parameters, the drive and response systems are synchronized. Synchronization between the fractional-order Chen chaotic system and the integer-order Chen chaotic system and between integer-order hyperchaotic Chen system and fractional-order hyperchaotic Rössler system is used to illustrate the effectiveness of the proposed synchronization approach. Numerical simulations coincide with the theoretical analysis.

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