scholarly journals Adaptive synchronization of a class of fractional order chaotic system with uncertain parameters

2015 ◽  
Vol 11 (6) ◽  
pp. 5306-5316
Author(s):  
De-fu Kong
Keyword(s):  
Parameter Identification ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Chaotic System ◽  
Stability Criterion ◽  
Local Stability ◽  
Adaptive Synchronization ◽  
Uncertain Parameters ◽  
Unknown Parameters ◽  
Control Scheme

In this manuscript, the adaptive synchronization of a class of fractional order chaotic system with uncertain parameters is studied. Firstly, the local stability of the fractional order chaotic system is analyzed using fractional stability criterion. Then, based on the J function criterion, suitable adaptive synchronization controller and parameter identification rules of the unknown parameters are investigated. Finally, the numerical simulations are presented to verify the effectiveness and robustness of the proposed control scheme.

Adaptive Synchronization of a Stochastic Fractional-Order System

2015 ◽  
Vol 733 ◽  
pp. 939-942
Author(s):  
Xiao Jun Liu
Keyword(s):  
Numerical Simulations ◽  
Fractional Order ◽  
Stochastic System ◽  
Fractional Order System ◽  
Adaptive Synchronization ◽  
Order System ◽  
Unknown Parameters ◽  
Adaptive Laws

In this paper, adaptive synchronization of a stochastic fractional-order system with unknown parameters is studied. Firstly, the stochastic system is reduced into the equivalent deterministic one with Laguerre approximation. Then, the synchronization for the system is realized by designing appropriate controllers and adaptive laws of the unknown parameters. Numerical simulations are carried out to demonstrate the effectiveness of the controllers and laws.

scholarly journals One Adaptive Synchronization Approach for Fractional-Order Chaotic System with Fractional-Order1

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Ping Zhou ◽  
Rongji Bai
Keyword(s):  
Numerical Simulations ◽  
Equilibrium Point ◽  
Fractional Order ◽  
Chaotic System ◽  
Stability Result ◽  
Adaptive Synchronization ◽  
Fractional Order Systems ◽  
Lorenz Chaotic System

Based on a new stability result of equilibrium point in nonlinear fractional-order systems for fractional-order lying in1<q<2, one adaptive synchronization approach is established. The adaptive synchronization for the fractional-order Lorenz chaotic system with fractional-order1<q<2is considered. Numerical simulations show the validity and feasibility of the proposed scheme.

Adaptive Synchronization of Fractional Hyper-Chaotic System with Unknown Parameters

2013 ◽  
Vol 850-851 ◽  
pp. 868-871 ◽  
Author(s):  
Li Xin Yang ◽  
Wan Sheng He ◽  
Jin Ping Jia ◽  
Fan Di Zhang
Keyword(s):  
Fractional Order ◽  
Tracking Control ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Adaptive Synchronization ◽  
Uncertain Parameters ◽  
Unknown Parameters ◽  
Fractional Systems ◽  
Control Approach ◽  
The Stability

In this paper, chaos synchronization of the modified Sprott E system is investigated. Based on the stability theorem for fractional systems, tracking control approach is used for the fractional-order systems with uncertain parameters. Meanwhile, suitable adaptive synchronization controller and recognizing rules of the uncertain parameters are designed. Numerical simulation results show that the method is easy to implement and reliable for synchronizing the two nonlinear fractional order hyper-chaotic systems.

scholarly journals Anti-Synchronization of a Class of Chaotic Systems with Application to Lorenz System: A Unified Analysis of the Integer Order and Fractional Order

Mathematics ◽  
2019 ◽  
Vol 7 (6) ◽  
pp. 559 ◽  
Author(s):  
Liang Chen ◽  
Chengdai Huang ◽  
Haidong Liu ◽  
Yonghui Xia
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Finite Time ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Unknown Parameters ◽  
Integer Order ◽  
System A ◽  
Control Scheme ◽  
Lorenz Chaotic System

The paper proves a unified analysis for finite-time anti-synchronization of a class of integer-order and fractional-order chaotic systems. We establish an effective controller to ensure that the chaotic system with unknown parameters achieves anti-synchronization in finite time under our controller. Then, we apply our results to the integer-order and fractional-order Lorenz system, respectively. Finally, numerical simulations are presented to show the feasibility of the proposed control scheme. At the same time, through the numerical simulation results, it is show that for the Lorenz chaotic system, when the order is greater, the more quickly is anti-synchronization achieved.

TWO ADAPTIVE SYNCHRONIZATION METHODS OF UNCERTAIN CHEN SYSTEM

2009 ◽  
Vol 23 (26) ◽  
pp. 5163-5169 ◽  
Author(s):  
XINGYUAN WANG ◽  
MIN XU ◽  
HUAGUANG ZHANG
Keyword(s):  
Numerical Simulations ◽  
Adaptive Synchronization ◽  
Uncertain Parameters ◽  
Unknown Parameters ◽  
Chen System ◽  
Synchronization Problem

This article addresses the adaptive synchronization problem of two Chen systems with uncertain parameters. Two adaptive synchronization methods are designed. In the two methods, we use only two controllers to synchronize uncertain Chen systems. It is theoretically proved that these two methods can make uncertain Chen systems asymptotically synchronized and identify the unknown parameters. Numerical simulations show the effectiveness of the proposed methods further. The comparisons of these two methods show: The method of theorem 1 is easier and more feasible than that of theorem 2, and the synchronization results are better.

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.

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