scholarly journals Dynamics Feature and Synchronization of a Robust Fractional-Order Chaotic System

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Xuan-Bing Yang ◽  
Yi-Gang He ◽  
Chun-Lai Li
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Phase Synchronization ◽  
Three Dimensional ◽  
Signal Amplitude ◽  
Projective Synchronization ◽  
Distribution Map ◽  
Variation Of Parameters ◽  
Synchronization Region ◽  
Control Scheme

Exploring the dynamics feature of robust chaotic system is an attractive yet recent topic of interest. In this paper, we introduce a three-dimensional fractional-order chaotic system. The important finding by analysis is that the position of signalx3descends at the speed of 1/cas the parameterbincreases, and the signal amplitude ofx1,x2can be controlled by the parametermin terms of the power function with the index −1/2. What is more, the dynamics remains constant with the variation of parametersbandm. Consequently, this system can provide rich encoding keys for chaotic communication. By considering the properties of amplitude and position modulation, the partial projective synchronization and partial phase synchronization are realized with linear control scheme. The distribution map of optimal synchronization region in the control-parameter space is charted by defining the power consumption of controller. Numerical simulations are executed to confirm the theoretical analysis.

Adaptive Sliding Mode Control for Synchronization of a Fractional-Order Chaotic System

2012 ◽  
Vol 8 (3) ◽  
Author(s):  
Chunlai Li ◽  
Kalin Su ◽  
Lei Wu
Keyword(s):  
Sliding Mode Control ◽  
Fractional Order ◽  
Chaotic System ◽  
Sliding Mode ◽  
Three Dimensional ◽  
Signal Amplitude ◽  
Adaptive Sliding Mode Control ◽  
Mode Control ◽  
Dynamical Behaviors ◽  
State Controller

This paper proposes a three-dimensional autonomous chaotic system which displays some interest dynamical behaviors such as invariable Lyapunov exponent spectrums and controllable signal amplitude. The corresponding fractional version of the proposed system is obtained. A single state controller for synchronization of this fractional-order chaotic system is developed based on the techniques of sliding mode control and adaptive control. Numerical simulations are provided to demonstrate the feasibility of the presented synchronization method.

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.

HYPERCHAOS IN THE FRACTIONAL-ORDER NONAUTONOMOUS CHEN'S SYSTEM AND ITS SYNCHRONIZATION

2005 ◽  
Vol 16 (05) ◽  
pp. 815-826 ◽  
Author(s):  
HONGBIN ZHANG ◽  
CHUNGUANG LI ◽  
GUANRONG CHEN ◽  
XING GAO
Keyword(s):  
Numerical Simulations ◽  
Fractional Order ◽  
Chaotic System ◽  
Three Dimensional ◽  
Synchronization Problem ◽  
Driving Signal

Recently, a new hyperchaos generator, obtained by controlling a three-dimensional autonomous chaotic system — Chen's system — with a periodic driving signal, has been found. In this letter, we formulate and study the hyperchaotic behaviors in the corresponding fractional-order hyperchaotic Chen's system. Through numerical simulations, we found that hyperchaos exists in the fractional-order hyperchaotic Chen's system with order less than 4. The lowest order we found to have hyperchaos in this system is 3.4. Finally, we study the synchronization problem of two fractional-order hyperchaotic Chen's systems.

Synchronization of Liu Chaotic System with Fractional-Order

2013 ◽  
Vol 336-338 ◽  
pp. 467-470
Author(s):  
Su Hai Huang
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Stability Theory ◽  
Unknown Parameter ◽  
Chaos Synchronization ◽  
Sliding Mode ◽  
Projective Synchronization ◽  
Sliding Mode Controller ◽  
Adaptive Sliding Mode ◽  
Adaptive Sliding Mode Controller

This paper deals with chaos synchronization of the Liu chaotic system with fractional-order. Based on the fractional-order stability theory, an adaptive sliding mode controller has been constructed to realize projective synchronization of fractional-order Liu chaotic system with unknown parameter. An illustrative simulation result is given to demonstrate the effectiveness of the proposed sliding mode controller.

scholarly journals Stabilization of the FO-BLDCM Chaotic System in the Sense of Lyapunov

2015 ◽  
Vol 2015 ◽  
pp. 1-5
Author(s):  
Ping Zhou ◽  
Rongji Bai ◽  
Hao Cai
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Direct Method ◽  
Order System ◽  
Lyapunov Direct Method ◽  
Brushless Dc Motors ◽  
Brushless Dc ◽  
Dc Motors ◽  
System A ◽  
Control Scheme

Based on an integer-order Brushless DC motors (IO-BLDCM) system, we give a fractional-order Brushless DC motors (FO-BLDCM) system in this paper. There exists a chaotic attractor for fractional-order0.95<q≤1in the FO-BLDCM system. Furthermore, using the Lyapunov direct method for fractional-order system, a control scheme is proposed to stabilize the FO-BLDCM chaotic system in the sense of Lyapunov. Numerical simulation shows that the control scheme in this paper is valid for the FO-BLDCM chaotic system.

Adaptive Projective Synchronization of the New Three-Dimensional Chaotic System

2013 ◽  
Vol 321-324 ◽  
pp. 921-924 ◽  
Author(s):  
Su Hai Huang
Keyword(s):  
Chaotic System ◽  
Finite Time ◽  
Chaos Synchronization ◽  
Three Dimensional ◽  
Projective Synchronization ◽  
Time Stability ◽  
Finite Time Stability ◽  
Adaptive Technique ◽  
New Chaotic System ◽  
Synchronization Scheme

This paper deals with the finite-time chaos synchronization of the new chaotic system [with uncertain parameters. Based on the finite-time stability theory and adaptive technique, a controller has been designed to realize finite-time chaos projective synchronization and parameter identification. Moreover, numerical simulation result is included to demonstrate the effectiveness and feasibility of the proposed synchronization scheme.

Sign in / Sign up

Export Citation Format

Share Document