DIVERSE STRUCTURE SYNCHRONIZATION OF FRACTIONAL ORDER HYPER-CHAOTIC SYSTEMS

2013 ◽  
Vol 27 (11) ◽  
pp. 1350034 ◽  
Author(s):  
XING-YUAN WANG ◽  
GUO-BIN ZHAO ◽  
YU-HONG YANG
Keyword(s):  
Numerical Analysis ◽  
Fractional Order ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Control Method ◽  
Rossler System ◽  
Rössler System ◽  
Predictor Corrector ◽  
Fractional Orders ◽  
Active Control Method

This paper studied the dynamic behavior of the fractional order hyper-chaotic Lorenz system and the fractional order hyper-chaotic Rössler system, then numerical analysis of the different fractional orders hyper-chaotic systems are carried out under the predictor–corrector method. We proved the two systems are in hyper-chaos when the maximum and the second largest Lyapunov exponential are calculated. Also the smallest orders of the systems are proved when they are in hyper-chaos. The diverse structure synchronization of the fractional order hyper-chaotic Lorenz system and the fractional order hyper-chaotic Rössler system is realized using active control method. Numerical simulations indicated that the scheme was always effective and efficient.

Reduced-order anti-synchronization of the projections of the fractional order hyperchaotic and chaotic systems

Open Physics ◽  
2013 ◽  
Vol 11 (10) ◽  
Author(s):  
Mayank Srivastava ◽  
Saurabh Agrawal ◽  
Subir Das
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Control Method ◽  
Sufficient Conditions ◽  
Transformation Theory ◽  
Reduced Order ◽  
Hyperchaotic Lorenz System ◽  
Fractional Orders ◽  
Active Control Method

AbstractThe article aims to study the reduced-order anti-synchronization between projections of fractional order hyperchaotic and chaotic systems using active control method. The technique is successfully applied for the pair of systems viz., fractional order hyperchaotic Lorenz system and fractional order chaotic Genesio-Tesi system. The sufficient conditions for achieving anti-synchronization between these two systems are derived via the Laplace transformation theory. The fractional derivative is described in Caputo sense. Applying the fractional calculus theory and computer simulation technique, it is found that hyperchaos and chaos exists in the fractional order Lorenz system and fractional order Genesio-Tesi system with order less than 4 and 3 respectively. The lowest fractional orders of hyperchaotic Lorenz system and chaotic Genesio-Tesi system are 3.92 and 2.79 respectively. Numerical simulation results which are carried out using Adams-Bashforth-Moulton method, shows that the method is reliable and effective for reduced order anti-synchronization.

Local Bifurcations and Chaos in the Fractional Rössler System

2018 ◽  
Vol 28 (08) ◽  
pp. 1850098 ◽  
Author(s):  
Jan Čermák ◽  
Luděk Nechvátal
Keyword(s):  
Fractional Order ◽  
Control Method ◽  
Chaotic Behavior ◽  
A Priori ◽  
Hopf Bifurcations ◽  
Rossler System ◽  
Master System ◽  
Rössler System ◽  
Active Control Method

The paper discusses the fractional Rössler system and the dependence of its dynamics on some entry parameters. An explicit algorithm for a priori determination of fractional Hopf bifurcations is derived and scenarios documenting a route of the system from stability to chaos are performed with respect to a varying system’s fractional order as well as to a varying system’s coefficient. Contrary to the existing results, the searched values of the fractional Hopf bifurcations follow directly from a revealed analytical dependence between these two systems’ entries. Their various critical values are established and confirmed by numerical experiments demonstrating not only the loss of stability of an equilibrium point, but also other phenomena of transition to chaotic behavior. In addition, we suggest an active control method for synchronization of two chaotic fractional-order Rössler systems. Our theoretical analysis enables to synchronize them for any value of a free parameter under which the master system displays a chaotic behavior.

Comparison of Times of Synchronization of Chaotic Burke-Shaw Attractor with Active Control and Integer and Optimum Fractional-Order Pecaro Carroll Method

2021 ◽  
Author(s):  
Ali Durdu ◽  
Yılmaz Uyaroğlu
Keyword(s):  
Active Control ◽  
Fractional Order ◽  
Chaotic Attractor ◽  
Secure Communication ◽  
Chaotic Systems ◽  
Control Method ◽  
Initial Conditions ◽  
Data Communication ◽  
Experimental Results ◽  
Active Control Method

Abstract Many studies have been introduced in the literature showing that two identical chaotic systems can be synchronized with different initial conditions. Secure data communication applications have also been made using synchronization methods. In the study, synchronization times of two popular synchronization methods are compared, which is an important issue for communication. Among the synchronization methods, active control, integer, and fractional-order Pecaro Carroll (P-C) method was used to synchronize the Burke-Shaw chaotic attractor. The experimental results showed that the P-C method with optimum fractional-order is synchronized in 2.35 times shorter time than the active control method. This shows that the P-C method using fractional-order creates less delay in synchronization and is more convenient to use in secure communication applications.

scholarly journals Complex Dynamics of the Fractional-Order Rössler System and Its Tracking Synchronization Control

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Huihai Wang ◽  
Shaobo He ◽  
Kehui Sun
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Complex Dynamics ◽  
Adomian Decomposition Method ◽  
Adomian Decomposition ◽  
Chaotic Signals ◽  
Rossler System ◽  
Master System ◽  
Rössler System ◽  
Tracking Synchronization

Numerical analysis of fractional-order chaotic systems is a hot topic of recent years. The fractional-order Rössler system is solved by a fast discrete iteration which is obtained from the Adomian decomposition method (ADM) and it is implemented on the DSP board. Complex dynamics of the fractional-order chaotic system are analyzed by means of Lyapunov exponent spectra, bifurcation diagrams, and phase diagrams. It shows that the system has rich dynamics with system parameters and the derivative order q. Moreover, tracking synchronization controllers are theoretically designed and numerically investigated. The system can track different signals including chaotic signals from the fractional-order master system and constant signals. It lays a foundation for the application of the fractional-order Rössler system.

scholarly journals Antisynchronization of Nonidentical Fractional-Order Chaotic Systems Using Active Control

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Sachin Bhalekar ◽  
Varsha Daftardar-Gejji
Keyword(s):  
Active Control ◽  
Fractional Order ◽  
Chaotic Systems ◽  
Control Method ◽  
Value Of Time ◽  
State Variables ◽  
Financial Systems ◽  
The Stability ◽  
First Time ◽  
Active Control Method

Antisynchronization phenomena are studied in nonidentical fractional-order differential systems. The characteristic feature of antisynchronization is that the sum of relevant state-variables vanishes for sufficiently large value of time variable. Active control method is used first time in the literature to achieve antisynchronization between fractional-order Lorenz and Financial systems, Financial and Chen systems, and Lü and Financial systems. The stability analysis is carried out using classical results. We also provide numerical results to verify the effectiveness of the proposed theory.

CHAOS SYNCHRONIZATION VIA CONTROLLING PARTIAL STATE OF CHAOTIC SYSTEMS

2001 ◽  
Vol 11 (06) ◽  
pp. 1737-1741 ◽  
Author(s):  
XINGHUO YU ◽  
YANXING SONG
Keyword(s):  
Invariant Manifold ◽  
Fourth Order ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Dynamic Properties ◽  
Rossler System ◽  
Rössler System ◽  
Partial State ◽  
The Lorenz System

An invariant manifold based chaos synchronization approach is proposed in this letter. A novel idea of using only a partial state of chaotic systems to synchronize the coupled chaotic systems is presented by taking into account the inherent dynamic properties of the chaotic systems. The effectiveness of the approach and idea is tested on the Lorenz system and the fourth-order Rossler system.

Comparative study of synchronization methods of fractional order chaotic systems

2016 ◽  
Vol 5 (3) ◽  
Author(s):  
Ajit K. Singh ◽  
Vijay K. Yadav ◽  
S. Das
Keyword(s):  
Active Control ◽  
Fractional Order ◽  
Chaotic Systems ◽  
Control Method ◽  
Salient Feature ◽  
Backstepping Method ◽  
Backstepping Approach ◽  
Active Control Method ◽  
Methods Numerical ◽  
Better Than

AbstractIn this article, the active control method and the backstepping method are used during the synchronization of fractional order chaotic systems. The salient feature of the article is the analysis of time of synchronization between fractional order Chen and Qi systems using both the methods. Numerical simulation and graphical results clearly exhibit that backstepping approach is better than active control method for synchronization of the considered pair of systems, as it takes less time to synchronize while using the first one compare to second one.

scholarly journals Phase and Antiphase Synchronization between 3-Cell CNN and Volta Fractional-Order Chaotic Systems via Active Control

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Zahra Yaghoubi ◽  
Hassan Zarabadipour
Keyword(s):  
Dynamical Systems ◽  
Active Control ◽  
Fractional Order ◽  
Chaotic Systems ◽  
Control Method ◽  
Secure Communications ◽  
Digital Signals ◽  
Chaotic Dynamical Systems ◽  
Synchronization Method ◽  
Active Control Method

Synchronization of fractional-order chaotic dynamical systems is receiving increasing attention owing to its interesting applications in secure communications of analog and digital signals and cryptographic systems. In this paper, a drive-response synchronization method is studied for “phase and antiphase synchronization” of a class of fractional-order chaotic systems via active control method, using the 3-cell and Volta systems as an example. These examples are used to illustrate the effectiveness of the synchronization method.

Anti-synchronization between identical and non-identical fractional-order chaotic systems using active control method

2013 ◽  
Vol 76 (2) ◽  
pp. 905-914 ◽  
Author(s):  
M. Srivastava ◽  
S. P. Ansari ◽  
S. K. Agrawal ◽  
S. Das ◽  
A. Y. T. Leung
Keyword(s):  
Active Control ◽  
Fractional Order ◽  
Chaotic Systems ◽  
Control Method ◽  
Active Control Method
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