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.

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.

ACTIVE CONTROL OF UNCERTAIN CHAOTIC SYSTEMS WITH PARAMETRIC PERTURBATION

2006 ◽  
Vol 20 (16) ◽  
pp. 2255-2264
Author(s):  
HAO ZHANG ◽  
XI-KUI MA
Keyword(s):  
Active Control ◽  
Control Strategy ◽  
Chaotic Systems ◽  
Control Method ◽  
Sufficient Condition ◽  
Parametric Perturbation ◽  
Uncertain Chaotic Systems ◽  
The Stability ◽  
Parameters Perturbation ◽  
Active Control Method

This paper presents an active control method for controlling general uncertain chaotic systems with parameters perturbation. And a sufficient condition is drawn for the stability of the controlled chaotic systems and is applied to guiding the design of the controllers. Finally, numerical results are used to show the robustness and effectiveness of the proposed control strategy.

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

scholarly journals CentrifugationSynchronization Control of Fractional Order Chaotic Systems Based on Memristor and Its Hardware Implementation

2021 ◽  
pp. 289-297
Author(s):  
Zhaohan zhang, Huiling Jin
Keyword(s):  
Fractional Order ◽  
Hardware Implementation ◽  
Chaotic Systems ◽  
Control Method ◽  
Sliding Mode ◽  
Sliding Mode Controller ◽  
Controlled System ◽  
Integer Order ◽  
The Stability ◽  
Dynamic Phenomena

This paper studies the synchronization control of fractional order chaotic systems based on memristor and its hardware implementation. This paper takes the complex dynamic phenomena of memristor turbidity system as the research background. Starting with the integer order memristor system, the fractional order form is derived based on the integer order turbid system, and its dynamics is deeply studied. At the same time, the turbidity phenomenon is applied to the watermark encryption algorithm, which effectively improves the confidentiality of the algorithm. Finally, in order to suppress the occurrence of turbidity, a fractional order sliding mode controller is proposed. In this paper, the sliding mode controller under the function switching control method is established, and the conditions for the parameters of the sliding mode controller are derived. Finally, the experimental results analyze the stability of the controlled system under different parameters, and give the corresponding time-domain waveform to verify the correctness of the theoretical analysis.

scholarly journals Robust Synchronisation of Uncertain Fractional-Order Chaotic Unified Systems

2017 ◽  
Vol 71 (1-2) ◽  
pp. 69-77
Author(s):  
Naeimadeen Noghredani ◽  
Saeed Balochian
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Financial Systems ◽  
External Disturbances ◽  
Sliding Mode Controllers ◽  
Error Dynamic ◽  
Error Dynamics ◽  
Integral Sliding Surface ◽  
The Stability

Abstract Fractional-order chaotic unified systems include a variety of fractional-order chaotic systems such as Chen, Lorenz, Lu, Liu, and financial systems. This paper describes a sliding mode controller for synchronisation of fractional-order chaotic unified systems in the presence of uncertainties and external disturbances, and affirms the stability of the controller (which is composed of error dynamics). Moreover, the synchronisation of two separate fractional-order chaotic systems is studied. For this aim, fractional integral sliding surface is defined. Then the sliding mode control rule for stability of error dynamic is presented based on the Lyapunov stability theorem. Simulation results, obtained by using MATLAB, show that the proposed sliding mode has employed an appropriate approach against uncertainties and to reduce the chattering phenomenon that often occurs with sliding mode controllers.

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