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.

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.

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.

GENERALIZED SYNCHRONIZATION OF NONIDENTICAL FRACTIONAL-ORDER CHAOTIC SYSTEMS

2013 ◽  
Vol 27 (30) ◽  
pp. 1350195 ◽  
Author(s):  
XING-YUAN WANG ◽  
ZUN-WEN HU ◽  
CHAO LUO
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Pole Placement ◽  
Generalized Synchronization ◽  
Chen System ◽  
Hyperchaotic Lorenz System ◽  
The Stability ◽  
Synchronization Scheme ◽  
Placement Technique

In this paper, a chaotic synchronization scheme is proposed to achieve the generalized synchronization between two different fractional-order chaotic systems. Based on the stability theory of fractional-order systems and the pole placement technique, a controller is designed and theoretical proof is given. Two groups of examples are shown to verify the effectiveness of the proposed scheme, the first one is to realize the generalized synchronization between the fractional-order Chen system and the fractional-order Rössler system, the second one is between the fractional-order Lü system and the fractional-order hyperchaotic Lorenz system. The corresponding numerical simulations verify the effectiveness of the proposed scheme.

scholarly journals Linear Control of Fractional-Order Financial Chaotic Systems with Input Saturation

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Junhai Luo ◽  
Guanjun Li ◽  
Heng Liu
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Control Method ◽  
Input Saturation ◽  
Sufficient Conditions ◽  
State Feedback Control ◽  
Linear Control ◽  
Control Input ◽  
Saturated Control ◽  
Laplace Transform Technique

In this paper, control of fractional-order financial chaotic systems with saturated control input is investigated by means of state-feedback control method. The saturation problem is tackled by using Gronwall-Bellman lemma and a memoryless nonlinearity function. Based on Gronwall inequality and Laplace transform technique, two sufficient conditions are achieved for the asymptotical stability of the fractional-order financial chaotic systems with fractional orders 0 <α≤ 1 and 1 <α< 2, respectively. Finally, simulation studies are carried out to show the effectiveness of the proposed linear control method.

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.

GENERALIZED (LAG, ANTICIPATED AND COMPLETE) PROJECTIVE SYNCHRONIZATION IN TWO NONIDENTICAL CHAOTIC SYSTEMS WITH UNKNOWN PARAMETERS

2012 ◽  
Vol 26 (16) ◽  
pp. 1250121
Author(s):  
XINGYUAN WANG ◽  
LULU WANG ◽  
DA LIN
Keyword(s):  
Adaptive Control ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Control Method ◽  
Projective Synchronization ◽  
Unknown Parameters ◽  
Chen System ◽  
Control Approach ◽  
Response System ◽  
Hyperchaotic Lorenz System

In this paper, a generalized (lag, anticipated and complete) projective synchronization for a general class of chaotic systems is defined. A systematic, powerful and concrete scheme is developed to investigate the generalized (lag, anticipated and complete) projective synchronization between the drive system and response system based on the adaptive control method and feedback control approach. The hyperchaotic Chen system and hyperchaotic Lorenz system are chosen to illustrate the proposed scheme. Numerical simulations are provided to show the effectiveness of the proposed schemes. In addition, the scheme can also be extended to research generalized (lag, anticipated and complete) projective synchronization between nonidentical discrete-time chaotic systems.

Using Active Sliding Mode Controller Antisynchronization of Fractional-Order Chaotic Systems with Uncertainties and Disturbances

2013 ◽  
Vol 411-414 ◽  
pp. 1779-1786
Author(s):  
Hong Zhang
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Control Method ◽  
Sliding Mode ◽  
Initial Conditions ◽  
Sufficient Conditions ◽  
External Disturbances ◽  
Active Sliding Mode Control ◽  
Derivative Method ◽  
Method Analysis

The antisynchronization behavior of fractional-order chaotic systems with parametric uncertainties and external disturbances is explored by using robust active sliding mode control method. The sufficient conditions for achieving robust antisynchronization of two identical fractional-order chaotic systems with different initial conditions and two different fractional-order chaotic systems with terms of uncertainties and external disturbances are derived based on the fractional-order derivative method. Analysis and numerical simulations are shown for validation purposes.

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.

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