scholarly journals Hybrid Projective Synchronization for Two Identical Fractional-Order Chaotic Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Ping Zhou ◽  
Rui Ding ◽  
Yu-xia Cao
Keyword(s):  
Fractional Order ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Projective Synchronization ◽  
Fractional Order Systems ◽  
Response System ◽  
Hyperchaotic Lu System ◽  
Hybrid Projective Synchronization ◽  
The Stability ◽  
Synchronization Scheme

A hybrid projective synchronization scheme for two identical fractional-order chaotic systems is proposed in this paper. Based on the stability theory of fractional-order systems, a controller for the synchronization of two identical fractional-order chaotic systems is designed. This synchronization scheme needs not to absorb all the nonlinear terms of response system. Hybrid projective synchronization for the fractional-order Chen chaotic system and hybrid projective synchronization for the fractional-order hyperchaotic Lu system are used to demonstrate the validity and feasibility of the proposed scheme.

GENERALIZED SYNCHRONIZATION OF FRACTIONAL ORDER CHAOTIC SYSTEMS

2011 ◽  
Vol 25 (09) ◽  
pp. 1283-1292 ◽  
Author(s):  
MING-JUN WANG ◽  
XING-YUAN WANG
Keyword(s):  
Theoretical Analysis ◽  
Fractional Order ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Chaotic Synchronization ◽  
Generalized Synchronization ◽  
Fractional Order Systems ◽  
Different Dimensions ◽  
The Stability ◽  
Synchronization Scheme

In the paper, generalized chaotic synchronization of a class of fractional order systems is studied. Based on the stability theory of linear fractional order systems, a generalized synchronization scheme is presented, and theoretical analysis is provided to verify its feasibility. The proposed method can realize generalized synchronization not only of fractional order systems with same dimension, but also of systems with different dimensions. Besides, the function relation of generalized synchronization can be linear or nonlinear. Numerical simulations show the effectiveness of the scheme.

PROJECTIVE SYNCHRONIZATION OF FRACTIONAL ORDER CHAOTIC SYSTEMS BASED ON STATE OBSERVER

2012 ◽  
Vol 26 (30) ◽  
pp. 1250176 ◽  
Author(s):  
XING-YUAN WANG ◽  
ZUN-WEN HU
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
State Observer ◽  
Projective Synchronization ◽  
Pole Placement ◽  
Fractional Order Systems ◽  
Chen System ◽  
The Stability ◽  
Synchronization Scheme ◽  
Placement Technique

Based on the stability theory of fractional order systems and the pole placement technique, this paper designs a synchronization scheme with the state observer method and achieves the projective synchronization of a class of fractional order chaotic systems. Taking an example for the fractional order unified system by using this observer controller, and numerical simulations of fractional order Lorenz-like system, fractional order Lü system and fractional order Chen system are provided to demonstrate the effectiveness of the proposed scheme.

scholarly journals Hybrid Projective Synchronization of Fractional-Order Chaotic Systems with Time Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Li-xin Yang ◽  
Jun Jiang
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Chaotic Systems ◽  
Projective Synchronization ◽  
Pole Placement ◽  
Fractional Order Systems ◽  
Hybrid Projective Synchronization ◽  
Synchronization Scheme ◽  
Hyperchaotic Systems ◽  
Placement Technique

The hybrid projective synchronization for fractional-order chaotic systems with time delay is investigated in this paper. On the basis of stability analysis of fractional-order systems and pole placement technique, a novel and general approach is proposed. The hybrid projective synchronization of fractional-order chaotic and hyperchaotic systems with time delay is achieved via designing an appropriate controller. Corresponding numerical results are presented to demonstrate the effectiveness of the proposed synchronization scheme. Furthermore, the influence of the fractional order on the synchronization process is discussed. The result reveals that the fractional order has a significant effect on the synchronization speed.

scholarly journals Modified Function Projective Synchronization between Different Dimension Fractional-Order Chaotic Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Ping Zhou ◽  
Rui Ding
Keyword(s):  
Numerical Simulations ◽  
Fractional Order ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Projective Synchronization ◽  
Fractional Order Systems ◽  
Fractional Order Derivative ◽  
Function Projective Synchronization ◽  
Modified Function Projective Synchronization ◽  
Synchronization Scheme

A modified function projective synchronization (MFPS) scheme for different dimension fractional-order chaotic systems is presented via fractional order derivative. The synchronization scheme, based on stability theory of nonlinear fractional-order systems, is theoretically rigorous. The numerical simulations demonstrate the validity and feasibility of the proposed method.

Hybrid Projective Synchronization for the Fractional-Order Chen-Lee System and its Circuit Realization

2013 ◽  
Vol 300-301 ◽  
pp. 1573-1578
Author(s):  
Seng Kin Lao ◽  
Hsien Keng Chen ◽  
Lap Mou Tam ◽  
Long Jye Sheu
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Body Motion ◽  
Projective Synchronization ◽  
Fractional Order Systems ◽  
Control Of Chaos ◽  
Circuit Realization ◽  
Hybrid Projective Synchronization ◽  
The Time Domain ◽  
Theoretical Analyses

The growing interest shows the importance of the control of chaos in fractional-order systems in recent years. This paper investigates in the hybrid projective synchronization of two chaotic systems with fractional-order, which were derived from Euler equations of rigid body motion. Theoretical analyses of the proposed methods are validated by numerical simulation in the time domain. Moreover, the synchronization system is realized using electronic circuits with fractance in the frequency domain.

SYNCHRONIZATION AND GENERALIZED SYNCHRONIZATION OF FRACTIONAL ORDER CHAOTIC SYSTEMS

2009 ◽  
Vol 23 (13) ◽  
pp. 1695-1714 ◽  
Author(s):  
XING-YUAN WANG ◽  
JING ZHANG
Keyword(s):  
Theoretical Analysis ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Stability Theory ◽  
Chaotic Systems ◽  
State Observer ◽  
Generalized Synchronization ◽  
Fractional Order Systems ◽  
The Stability

In this paper, based on the modified state observer method, synchronization and generalized synchronization of a class of fractional order chaotic systems are presented. The two synchronization approaches are theoretically and numerically studied and two simple criterions are proposed. By using the stability theory of linear fractional order systems, suitable conditions for achieving synchronization and generalized synchronization are given. Numerical simulations coincide with the theoretical analysis.

Hybrid Projective Synchronization of Complex Dynamical Networks with Fractional-Order System Nodes

2013 ◽  
Vol 336-338 ◽  
pp. 2365-2368
Author(s):  
Fan Di Zhang
Keyword(s):  
Fractional Order ◽  
Complex Dynamical Networks ◽  
Projective Synchronization ◽  
Control Technique ◽  
Order System ◽  
Dynamical Networks ◽  
Hybrid Projective Synchronization ◽  
The Stability ◽  
System Nodes ◽  
Synchronization Scheme

This paper investigates the problem of hybrid projective synchronization (HPS) in dynamical networks with fractional-order hyper-chaotic system nodes. Based on the stability analysis of fractional-order systems and nonlinear control technique, we propose a novel and general approach to realize the synchronization of complex network. A nonlinear controllers are designed to make the fractional-order complex dynamical networks with distinct nodes asymptotically synchronize onto any smooth goal dynamics. Numerical simulations are presented to demonstrate the effectiveness of the proposed synchronization scheme.

A New Method for Full State Hybrid Projective Synchronization of Different Fractional Order Chaotic Systems

2013 ◽  
Vol 385-386 ◽  
pp. 919-922 ◽  
Author(s):  
Hao Feng ◽  
Yang Yang ◽  
Shi Ping Yang
Keyword(s):  
Fractional Order ◽  
Feedback Linearization ◽  
Chaotic Systems ◽  
New Method ◽  
Projective Synchronization ◽  
Chen System ◽  
Full State ◽  
Error System ◽  
Hybrid Projective Synchronization ◽  
Synchronization Scheme

In this paper, the full state hybrid projective synchronization (FSHPS) between two different fractional order chaotic systems is investigated. i.e., the fractional order Chen system and the fractional order Lorenz system. Based on the synchronization error system feedback linearization theory, a new method combining feedback control is proposed for theFSHPSin fractional order chaotic systems. Numerical simulations are presented to verify the effectiveness and the feasibility of the synchronization scheme.

Hybrid Projective Synchronization of Different Fractional Order Hyperchaotic Systems

2014 ◽  
Vol 926-930 ◽  
pp. 3046-3049
Author(s):  
Jin Ping Jia ◽  
Fan Di Zhang
Keyword(s):  
Numerical Simulation ◽  
Active Control ◽  
Fractional Order ◽  
Stability Theory ◽  
Projective Synchronization ◽  
Order System ◽  
Simulation Results ◽  
Hybrid Projective Synchronization ◽  
The Stability ◽  
Hyperchaotic Systems

This paper investigated hybrid projective synchronization of fractional order hyperchaotic systems with different orders. Based on the idea of active control and the stability theory of linear fractional-order system, we design the effective controller to realize the hybrid projective synchronization. Numerical simulation results which are carried show that the method is easy to implement and reliable for synchronizing the two nonlinear fractional order hyperchaotic systems while it also allows both the systems to remain in hyperchaotic states.

scholarly journals Active Sliding Mode for Synchronization of a Wide Class of Four-Dimensional Fractional-Order Chaotic Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Bin Wang ◽  
Yuangui Zhou ◽  
Jianyi Xue ◽  
Delan Zhu
Keyword(s):  
Sliding Mode Control ◽  
Fractional Order ◽  
Wide Class ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Order System ◽  
Fractional Order Calculus ◽  
Simulation Results ◽  
The Stability

We focus on the synchronization of a wide class of four-dimensional (4-D) chaotic systems. Firstly, based on the stability theory in fractional-order calculus and sliding mode control, a new method is derived to make the synchronization of a wide class of fractional-order chaotic systems. Furthermore, the method guarantees the synchronization between an integer-order system and a fraction-order system and the synchronization between two fractional-order chaotic systems with different orders. Finally, three examples are presented to illustrate the effectiveness of the proposed scheme and simulation results are given to demonstrate the effectiveness of the proposed method.

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