Existence of Chaos, dynamical behaviour with fractional order derivatives and modified adaptive function projective synchronization with uncertain parameters of a chaotic system

Optik ◽  
2017 ◽  
Vol 131 ◽  
pp. 89-103 ◽  
Author(s):  
S.K. Agrawal ◽  
K. Vishal
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Dynamical Behaviour ◽  
Projective Synchronization ◽  
Uncertain Parameters ◽  
Adaptive Function ◽  
Function Projective Synchronization

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 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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