scholarly journals Compound Generalized Function Projective Synchronization for Fractional-Order Chaotic Systems

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Chunde Yang ◽  
Hao Cai ◽  
Ping Zhou
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Drive System ◽  
Projective Synchronization ◽  
Order System ◽  
Generalized Function ◽  
Function Projective Synchronization ◽  
The Stability ◽  
Generalized Function Projective Synchronization

A modified function projective synchronization for fractional-order chaotic system, called compound generalized function projective synchronization (CGFPS), is proposed theoretically in this paper. There are one scaling-drive system, more than one base-drive system, and one response system in the scheme of CGFPS, and the scaling function matrices come from multidrive systems. The proposed CGFPS technique is based on the stability theory of fractional-order system. Moreover, we achieve the CGFPS between three-driver chaotic systems, that is, the fractional-order Arneodo chaotic system, the fractional-order Chen chaotic system, and the fractional-order Lu chaotic system, and one response chaotic system, that is, the fractional-order Lorenz chaotic system. Numerical experiments are demonstrated to verify the effectiveness of the CGFPS scheme.

scholarly journals Sliding Mode Control and Modified Generalized Projective Synchronization of a New Fractional-Order Chaotic System

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Junbiao Guan ◽  
Kaihua Wang
Keyword(s):  
Sliding Mode Control ◽  
Fractional Order ◽  
Chaotic System ◽  
Secure Communication ◽  
Sliding Mode ◽  
Projective Synchronization ◽  
Control Technique ◽  
Order System ◽  
Mode Control ◽  
The Stability

A new fractional-order chaotic system is addressed in this paper. By applying the continuous frequency distribution theory, the indirect Lyapunov stability of this system is investigated based on sliding mode control technique. The adaptive laws are designed to guarantee the stability of the system with the uncertainty and external disturbance. Moreover, the modified generalized projection synchronization (MGPS) of the fractional-order chaotic systems is discussed based on the stability theory of fractional-order system, which may provide potential applications in secure communication. Finally, some numerical simulations are presented to show the effectiveness of the theoretical results.

Function Synchronization of the Fractional-Order Chaotic System

2013 ◽  
Vol 631-632 ◽  
pp. 1220-1225 ◽  
Author(s):  
J.W. Fan ◽  
N. Zhao ◽  
Y. Gao ◽  
H.L. Lan
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Error Function ◽  
Drive System ◽  
Order System ◽  
Secure Communications ◽  
Response System ◽  
Set Up ◽  
The Stability ◽  
Function Synchronization

Function synchronization is an important type of chaos synchronization because of enhancing the security of communication. In order to obtain the better conformances of function synchronization, a method of the fractional-order chaotic system is presented, which based on the stability theory of the fractional order system. This method need construct a parameter matrix and a coupled matrix using fractional-order chaotic drive system at first, and then the chaotic response system is set up with these matrixes. The synchronization error function between drive system and response system is satisfied with the asymptotic stability. Function synchronization of the fractional-order Rikitake chaotic system is selected as a typical example. Numerical simulation results demonstrate the validity of the presented method. This method not only has better synchronization conformances, but also can be applied in the chaotic secure communications.

scholarly journals Modified Function Projective Synchronization of Fractional Order Chaotic Systems with Different Dimensions

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Hong-Juan Liu ◽  
Zhi-Liang Zhu ◽  
Hai Yu ◽  
Qian Zhu
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Projective Synchronization ◽  
Hyperchaotic System ◽  
Unknown Parameters ◽  
Adaptive Controllers ◽  
Function Projective Synchronization ◽  
Modified Function Projective Synchronization ◽  
Different Dimensions ◽  
The Stability

The modified function projective synchronization of different dimensional fractional-order chaotic systems with known or unknown parameters is investigated in this paper. Based on the stability theorem of linear fractional-order systems, the adaptive controllers with corresponding parameter update laws for achieving the synchronization are given. The fractional-order chaotic system and hyperchaotic system are applied to achieve synchronization in both reduced order and increased order. The corresponding numerical results coincide with theoretical analysis.

scholarly journals Modified Function Projective Synchronization for a Partially Linear and Fractional-Order Financial Chaotic System with Uncertain Parameters

2017 ◽  
Vol 2017 ◽  
pp. 1-8
Author(s):  
Yehong Yang ◽  
Guohua Cao
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Projective Synchronization ◽  
Uncertain Parameters ◽  
Lyapunov Matrix Equation ◽  
Function Projective Synchronization ◽  
Partially Linear ◽  
Modified Function Projective Synchronization ◽  
Lyapunov Matrix ◽  
The Stability

This paper investigates the modified function projective synchronization between fractional-order chaotic systems, which are partially linear financial systems with uncertain parameters. Based on the stability theory of fractional-order systems and the Lyapunov matrix equation, a controller is obtained for the synchronization between fractional-order financial chaotic systems. Using the controller, the error systems converged to zero as time tends to infinity, and the uncertain parameters were also estimated so that the phenomenon of parameter distortion was effectively avoided. Numerical simulations demonstrate the validity and feasibility of the proposed method.

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