Combination synchronization of different dimensions fractional-order non-autonomous chaotic systems using scaling matrix

2020 ◽  
Author(s):  
Hadjer Zerimeche ◽  
Tarek Houmor ◽  
Abdelhak Berkane
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Combination Synchronization ◽  
Different Dimensions ◽  
Scaling Matrix

GENERALIZED SYNCHRONIZATION OF FRACTIONAL ORDER CHAOTIC SYSTEMS

2011 ◽  
Vol 25 (09) ◽  
pp. 1283-1292 ◽  
Author(s):  
MING-JUN WANG ◽  
XING-YUAN WANG
Keyword(s):  
Theoretical Analysis ◽  
Fractional Order ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Chaotic Synchronization ◽  
Generalized Synchronization ◽  
Fractional Order Systems ◽  
Different Dimensions ◽  
The Stability ◽  
Synchronization Scheme

In the paper, generalized chaotic synchronization of a class of fractional order systems is studied. Based on the stability theory of linear fractional order systems, a generalized synchronization scheme is presented, and theoretical analysis is provided to verify its feasibility. The proposed method can realize generalized synchronization not only of fractional order systems with same dimension, but also of systems with different dimensions. Besides, the function relation of generalized synchronization can be linear or nonlinear. Numerical simulations show the effectiveness of the scheme.

scholarly journals Combination synchronization of fractional order n-chaotic systems using active backstepping design

2019 ◽  
Vol 8 (1) ◽  
pp. 597-608 ◽  
Author(s):  
Vijay K. Yadav ◽  
S. Das
Keyword(s):  
Numerical Simulation ◽  
Lyapunov Function ◽  
Fractional Order ◽  
Chaotic Systems ◽  
Design Method ◽  
Backstepping Design ◽  
Fractional Order Systems ◽  
Combination Synchronization

Abstract In this article, a scheme using active backstepping design method is proposed to achieve combination synchronization of n number of fractional order chaotic systems. In the proposed method the controllers are designed with the help of a new lemma and Lyapunov function in a systematic way. Synchronization among three/four fractional order systems have been shown as examples of synchronization of n-chaotic systems. Numerical simulation and graphical results clearly exhibit that the method of this new procedure is easy to implement and reliable for synchronization of fractional order chaotic systems.

scholarly journals Special Characteristics and Synchronizations of Multi Hybrid-Order Chaotic Systems

Entropy ◽  
2020 ◽  
Vol 22 (6) ◽  
pp. 664
Author(s):  
Jiaxun Liu ◽  
Zuoxun Wang ◽  
Fangfang Zhang ◽  
Yankai Yin ◽  
Fengying Ma
Keyword(s):  
Fractional Order ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Combination Synchronization ◽  
Simulation Results ◽  
Total Dimension ◽  
Hybrid Forms

Based on advantages of integer and fractional chaotic systems, hybrid chaotic systems and their definitions and some fundamental concepts are proposed, such as hybrid degree (HD), the lowest order (LO) and the total dimension order (TDO). The preliminary properties of hybrid Lorenz systems and hybrid forms of some classic chaotic systems are studied. Then, the relations between HD, LO and TDO with different parameters is investigated in chaotic systems. To be specific, HD is associated with fractional order. It is a directional method to search LO and TDO in chaotic systems. Finally, based on the incommensurate fractional stability theory, we accomplish combination synchronization for three different hybrid order chaotic systems. The simulation results verify the effectiveness of the synchronization controller.

Sign in / Sign up

Export Citation Format

Share Document