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.

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 The Co-existence of Different Synchronization Types in Fractional-order Discrete-time Chaotic Systems with Non–identical Dimensions and Orders

Entropy ◽  
2018 ◽  
Vol 20 (9) ◽  
pp. 710 ◽  
Author(s):  
Samir Bendoukha ◽  
Adel Ouannas ◽  
Xiong Wang ◽  
Amina-Aicha Khennaoui ◽  
Viet-Thanh Pham ◽  
...  
Keyword(s):  
Nonlinear Control ◽  
Fractional Order ◽  
Discrete Time ◽  
Chaotic Systems ◽  
Projective Synchronization ◽  
Generalized Synchronization ◽  
Control Scheme ◽  
Full State ◽  
Hybrid Projective Synchronization ◽  
Inverse Generalized Synchronization

This paper is concerned with the co-existence of different synchronization types for fractional-order discrete-time chaotic systems with different dimensions. In particular, we show that through appropriate nonlinear control, projective synchronization (PS), full state hybrid projective synchronization (FSHPS), and generalized synchronization (GS) can be achieved simultaneously. A second nonlinear control scheme is developed whereby inverse full state hybrid projective synchronization (IFSHPS) and inverse generalized synchronization (IGS) are shown to co-exist. Numerical examples are presented to confirm the findings.

LAG FULL STATE HYBRID PROJECTIVE SYNCHRONIZATION IN DIFFERENT FRACTIONAL-ORDER CHAOTIC SYSTEMS

2010 ◽  
Vol 24 (31) ◽  
pp. 6129-6141 ◽  
Author(s):  
YANG TANG ◽  
JIAN-AN FANG ◽  
LIANG CHEN
Keyword(s):  
Control Theory ◽  
Numerical Simulations ◽  
Active Control ◽  
Fractional Order ◽  
Chaotic Systems ◽  
Projective Synchronization ◽  
Full State ◽  
Hybrid Projective Synchronization

In this paper, lag full state hybrid projective synchronization (LFSHPS) in fractional-order chaotic systems is first studied. We show that LFSHPS does exist in fractional-order chaotic systems. Based on active control theory, synchronization schemes for LFSHPS of the fractional-order chaotic systems are given. Numerical simulations are provided to illustrate and verify the effectiveness of the proposed methods.

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.

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