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.

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.

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 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.

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.

scholarly journals Synchronization of Fractional-Order Complex Chaotic Systems Based on Observers

Entropy ◽  
2019 ◽  
Vol 21 (5) ◽  
pp. 481 ◽  
Author(s):  
Zhonghui Li ◽  
Tongshui Xia ◽  
Cuimei Jiang
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Projective Synchronization ◽  
Pole Placement ◽  
Order Complex ◽  
Order Error ◽  
New Type ◽  
Modified Projective Synchronization ◽  
The Stability ◽  
Complex Chaotic Systems

By designing a state observer, a new type of synchronization named complex modified projective synchronization is investigated in a class of nonlinear fractional-order complex chaotic systems. Combining stability results of the fractional-order systems and the pole placement method, this paper proves the stability of fractional-order error systems and realizes complex modified projective synchronization. This method is so effective that it can be applied in engineering. Additionally, the proposed synchronization strategy is suitable for all fractional-order chaotic systems, including fractional-order hyper-chaotic systems. Finally, two numerical examples are studied to show the correctness of this new synchronization strategy.

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 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.

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.

GENERALIZED PROJECTIVE SYNCHRONIZATION OF CHAOTIC NEURAL NETWORKS: OBSERVER-BASED APPROACH

2010 ◽  
Vol 24 (17) ◽  
pp. 3351-3363 ◽  
Author(s):  
XING YUAN WANG ◽  
JUAN MENG
Keyword(s):  
Neural Networks ◽  
Numerical Simulations ◽  
State Observer ◽  
Projective Synchronization ◽  
Pole Placement ◽  
Chaotic Neural Networks ◽  
Generalized Projective Synchronization ◽  
Synchronization Scheme ◽  
Placement Technique ◽  
Nonlinear State

In this paper, the generalized projective synchronization of chaotic neural networks is investigated. Based on the modified nonlinear state observer algorithm and the pole placement technique, a synchronization scheme is designed. The generalized projective synchronization of different chaotic neural networks can be achieved by using the proposed method. Numerical simulations further demonstrate the effectiveness of the proposed 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.

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