Control and synchronization of fractional unified chaotic systems via active control technique

2014 ◽  
Author(s):  
Jian Yuan ◽  
Bao Shi
Keyword(s):  
Active Control ◽  
Chaotic Systems ◽  
Control Technique ◽  
Unified Chaotic Systems ◽  
Control And Synchronization

A study of a modified nonlinear dynamical system with fractal-fractional derivative

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Sunil Kumar ◽  
R.P. Chauhan ◽  
Shaher Momani ◽  
Samir Hadid
Keyword(s):  
Dynamical System ◽  
Fractional Derivative ◽  
Active Control ◽  
Numerical Scheme ◽  
Chaos Control ◽  
Nonlinear Dynamical System ◽  
Control Technique ◽  
Complex Behavior ◽  
Content Type ◽  
Control And Synchronization

Purpose This paper aims to study the complex behavior of a dynamical system using fractional and fractal-fractional (FF) derivative operators. The non-classical derivatives are extremely useful for investigating the hidden behavior of the systems. The Atangana–Baleanu (AB) and Caputo–Fabrizio (CF) derivatives are considered for the fractional structure of the model. Further, to add more complexity, the authors have taken the system with a CF fractal-fractional derivative having an exponential kernel. The active control technique is also considered for chaos control. Design/methodology/approach The systems under consideration are solved numerically. The authors show the Adams-type predictor-corrector scheme for the AB model and the Adams–Bashforth scheme for the CF model. The convergence and stability results are given for the numerical scheme. A numerical scheme for the FF model is also presented. Further, an active control scheme is used for chaos control and synchronization of the systems. Findings Simulations of the obtained solutions are displayed via graphics. The proposed system exhibits a very complex phenomenon known as chaos. The importance of the fractional and fractal order can be seen in the presented graphics. Furthermore, chaos control and synchronization between two identical fractional-order systems are achieved. Originality/value This paper mentioned the complex behavior of a dynamical system with fractional and fractal-fractional operators. Chaos control and synchronization using active control are also described.

Active Control for Multi-Switching Combination Synchronization of Non-Identical Chaotic Systems

2018 ◽  
pp. 129-162 ◽  
Author(s):  
Shikha Singh ◽  
Ahmad Taher Azar ◽  
Muzaffar Ahmad Bhat ◽  
Sundarapandian Vaidyanathan ◽  
Adel Ouannas
Keyword(s):  
Information Security ◽  
Numerical Simulations ◽  
Active Control ◽  
Chaotic Systems ◽  
Control Technique ◽  
Slave System ◽  
Combination Synchronization ◽  
Wide Range ◽  
Synchronization Scheme ◽  
Theoretical Results

This chapter investigates the multi-switching combination synchronization of three non-identical chaotic systems via active control technique. In recent years, some advances have been made with the idea of multi-switching combination synchronization. The different states of the master systems are synchronized with the desired state of the slave system in multi-switching combination synchronization scheme. The relevance of such kinds of synchronization studies to information security is evident in the wide range of possible synchronization directions that exist due to multi-switching synchronization. Numerical simulations justify the validity of the theoretical results discussed.

Synchronization of the unified chaotic systems via active control

2006 ◽  
Vol 27 (5) ◽  
pp. 1292-1297 ◽  
Author(s):  
Ahmet Uçar ◽  
Karl E. Lonngren ◽  
Er-Wei Bai
Keyword(s):  
Active Control ◽  
Chaotic Systems ◽  
Unified Chaotic Systems

scholarly journals STABILITY OF THE CONTROLLED SYNCHRONIZATION MANIFOLD IN A RING OF MUTUALLY COUPLED CHAOTIC SYSTEMS

2008 ◽  
Vol 18 (08) ◽  
pp. 2397-2414
Author(s):  
R. YAMAPI ◽  
M. A. AZIZ-ALAOUI
Keyword(s):  
Active Control ◽  
Chaotic Systems ◽  
Control Technique ◽  
Control Gain ◽  
Invariant Ring ◽  
Coupling Parameters ◽  
Single Oscillator ◽  
The Stability ◽  
Bifurcation Structures ◽  
Synchronization Manifold

The active control of the unstable synchronization manifold in a shift-invariant ring of N mutually coupled chaotic oscillators is investigated. After deriving the bifurcation structures and chaotic states in the single oscillator, we find the regime of coupling parameters leading to stable and unstable synchronization phenomena in the ring, using the Master stability function approach with the transverse Lyapunov exponents. The active control technique is applied on the mutually coupled chaotic systems to suppress unstable synchronization states. We derive the range of control gain parameters which leads to a successful control and the stability of the control design. The effects of the amplitude of the parametric perturbations on the stability boundaries of the controlled unstable synchronization process are also studied.

scholarly journals Synchronization of Different Fractional Order Time-Delay Chaotic Systems Using Active Control

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Jianeng Tang
Keyword(s):  
Time Delay ◽  
Laplace Transform ◽  
Numerical Simulations ◽  
Active Control ◽  
Fractional Order ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Control Technique ◽  
The Laplace Transform

Chaos synchronization of different fractional order time-delay chaotic systems is considered. Based on the Laplace transform theory, the conditions for achieving synchronization of different fractional order time-delay chaotic systems are analyzed by use of active control technique. Then numerical simulations are provided to verify the effectiveness and feasibility of the developed method. At last, effects of the fraction order and the time delay on synchronization are further researched.

scholarly journals Hybrid synchronisation of vallis chaotic systems using nonlinear active control

2018 ◽  
Vol 7 (2.21) ◽  
pp. 50 ◽  
Author(s):  
Piyush Pratap Singh ◽  
Vikash Kumar ◽  
Eshan Tiwari ◽  
Vinay K. Chauhan
Keyword(s):  
Numerical Simulation ◽  
Active Control ◽  
Lyapunov Stability ◽  
Chaotic Systems ◽  
Southern Oscillation ◽  
Lyapunov Stability Theory ◽  
Control Technique ◽  
Control Laws ◽  
Relevant Variables ◽  
Simulation Results

In this paper, hybrid synchronisation of Vallis chaotic systems using a nonlinear control technique is proposed. Vallis system represents the principal quantitative features of the El-Nino Southern Oscillation (ENSO) phenomenon. A nonlinear active control technique is used for hybrid synchronisation. Control laws are designed by using the sum of the relevant variables of the both mater and slave systems. Required Lyapunov stability condition is devised using Lyapunov stability theory. Numerical simulation results reflect the successful achievement of the proposed objectives. MATLAB is used for simulation.  

Synchronization of Different Fractional Order Time-Delay Chaotic Systems Using Active Control

2013 ◽  
Vol 805-806 ◽  
pp. 1975-1978
Author(s):  
Jia Neng Tang
Keyword(s):  
Time Delay ◽  
Laplace Transform ◽  
Numerical Simulations ◽  
Active Control ◽  
Fractional Order ◽  
Chaotic Systems ◽  
Control Technique ◽  
The Laplace Transform

In this paper, based on the Laplace transform theory, the conditions for achieving synchronization of different fractional order time-delay chaotic systems are analyzed by use of active control technique. Then numerical simulations are provided to verify the effectiveness and feasibility of the developed method.

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