scholarly journals Dynamics, Chaos Control, and Synchronization in a Fractional-Order Samardzija-Greller Population System with Order Lying in (0, 2)

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
A. Al-khedhairi ◽  
S. S. Askar ◽  
A. E. Matouk ◽  
A. Elsadany ◽  
M. Ghazel
Keyword(s):  
Fractional Order ◽  
Chaos Control ◽  
Control Method ◽  
Control Technique ◽  
Linear Feedback ◽  
Nonlinear Feedback ◽  
Population System ◽  
Wide Range ◽  
Control And Synchronization ◽  
Fractional Parameter

This paper demonstrates dynamics, chaos control, and synchronization in Samardzija-Greller population model with fractional order between zero and two. The fractional-order case is shown to exhibit rich variety of nonlinear dynamics. Lyapunov exponents are calculated to confirm the existence of wide range of chaotic dynamics in this system. Chaos control in this model is achieved via a novel linear control technique with the fractional order lying in (1, 2). Moreover, a linear feedback control method is used to control the fractional-order model to its steady states when 0<α<2. In addition, the obtained results illustrate the role of fractional parameter on controlling chaos in this model. Furthermore, nonlinear feedback synchronization scheme is also employed to illustrate that the fractional parameter has a stabilizing role on the synchronization process in this system. The analytical results are confirmed by numerical simulations.

scholarly journals Chaos Control and Synchronization in Fractional-Order Lorenz-Like System

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Sachin Bhalekar
Keyword(s):  
Dynamical System ◽  
Fractional Order ◽  
Chaos Control ◽  
Chaotic Behavior ◽  
Stable Region ◽  
Linear Feedback ◽  
Effective Dimension ◽  
Nonlinear Feedback ◽  
Linear Feedback Controller ◽  
Control And Synchronization

The present paper deals with fractional-order version of a dynamical system introduced by Chongxin et al. (2006). The chaotic behavior of the system is studied using analytic and numerical methods. The minimum effective dimension is identified for chaos to exist. The chaos in the proposed system is controlled using simple linear feedback controller. We design a controller to place the eigenvalues of the system Jacobian in a stable region. The effectiveness of the controller in eliminating the chaotic behavior from the state trajectories is also demonstrated using numerical simulations. Furthermore, we synchronize the system using nonlinear feedback.

scholarly journals Chaos Control in Mechanical Systems

2006 ◽  
Vol 13 (4-5) ◽  
pp. 301-314 ◽  
Author(s):  
Marcelo A. Savi ◽  
Francisco Heitor I. Pereira-Pinto ◽  
Armando M. Ferreira
Keyword(s):  
Chaos Control ◽  
Control Method ◽  
Chaotic Behavior ◽  
Mechanical Systems ◽  
Control Technique ◽  
Continuous Control ◽  
State Variables ◽  
Unstable Periodic Orbits ◽  
State Observers ◽  
Wide Range

Chaos has an intrinsically richness related to its structure and, because of that, there are benefits for a natural system of adopting chaotic regimes with their wide range of potential behaviors. Under this condition, the system may quickly react to some new situation, changing conditions and their response. Therefore, chaos and many regulatory mechanisms control the dynamics of living systems, conferring a great flexibility to the system. Inspired by nature, the idea that chaotic behavior may be controlled by small perturbations of some physical parameter is making this kind of behavior to be desirable in different applications. Mechanical systems constitute a class of system where it is possible to exploit these ideas. Chaos control usually involves two steps. In the first, unstable periodic orbits (UPOs) that are embedded in the chaotic set are identified. After that, a control technique is employed in order to stabilize a desirable orbit. This contribution employs the close-return method to identify UPOs and a semi-continuous control method, which is built up on the OGY method, to stabilize some desirable UPO. As an application to a mechanical system, a nonlinear pendulum is considered and, based on parameters obtained from an experimental setup, analyses are carried out. Signals are generated by numerical integration of the mathematical model and two different situations are treated. Firstly, it is assumed that all state variables are available. After that, the analysis is done from scalar time series and therefore, it is important to evaluate the effect of state space reconstruction. Delay coordinates method and extended state observers are employed with this aim. Results show situations where these techniques may be used to control chaos in mechanical systems.

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.

scholarly journals The Robust Control and Synchronization of a Class of Fractional-Order Chaotic Systems with External Disturbances via a Single Output

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Runzi Luo ◽  
Haipeng Su
Keyword(s):  
Robust Control ◽  
Fractional Order ◽  
Chaos Control ◽  
Chaotic Systems ◽  
Sufficient Conditions ◽  
External Disturbances ◽  
Numerical Examples ◽  
Single Output ◽  
Lorenz Chaotic System ◽  
Control And Synchronization

This paper investigates the stabilization and synchronization of a class of fractional-order chaotic systems which are affected by external disturbances. The chaotic systems are assumed that only a single output can be used to design the controller. In order to design the proper controller, some observer systems are proposed. By using the observer systems some sufficient conditions for achieving chaos control and synchronization of fractional-order chaotic systems are derived. Numerical examples are presented by taking the fractional-order generalized Lorenz chaotic system as an example to show the feasibility and validity of the proposed method.

Complexity of Nonlinear Dynamic Outputs Model in the Electricity Triopoly

2014 ◽  
Vol 1008-1009 ◽  
pp. 1395-1398
Author(s):  
Wei Zhuo Ji
Keyword(s):  
Electric Power ◽  
Dynamic Model ◽  
Nonlinear Dynamic ◽  
Chaos Control ◽  
Control Method ◽  
Repeated Game ◽  
Game Model ◽  
Nonlinear Feedback ◽  
Nonlinear Dynamic Model

A dynamic repeated model has been established in electric power Triopoly. The chaos and density cycling of the nonlinear dynamic model are investigated in detail. The nonlinear feedback chaos control method is successfully applied to the dynamic repeated game model.

TIME DELAYED REPETITIVE LEARNING CONTROL FOR CHAOTIC SYSTEMS

2002 ◽  
Vol 12 (05) ◽  
pp. 1057-1065 ◽  
Author(s):  
YANXING SONG ◽  
XINGHUO YU ◽  
GUANRONG CHEN ◽  
JIAN-XIN XU ◽  
YU-PING TIAN
Keyword(s):  
Periodic Orbits ◽  
Adaptive Learning ◽  
Chaos Control ◽  
Chaotic Systems ◽  
Control Method ◽  
Learning Control ◽  
Control Technique ◽  
Unstable Periodic Orbits ◽  
Repetitive Learning ◽  
Control Principle

In this paper, a time-delayed chaos control method based on repetitive learning is proposed. A general repetitive learning control structure based on the invariant manifold of the chaotic system is given. The integration of the repetitive learning control principle and the time-delayed chaos control technique enables adaptive learning of appropriate control actions from learning cycles. In contrast to the conventional repetitive learning control, no exact knowledge (analytic representation) of the target unstable periodic orbits is needed, except for the time delay constant, which can be identified via either experiments or adaptive learning. The controller effectively stabilizes the states of the continuous-time chaos on desired unstable periodic orbits. Simulations on the Duffing and Lorenz chaotic systems are provided to verify the design and analysis.

scholarly journals Control and Synchronization of Chaos in RCL-Shunted Josephson Junction with Noise Disturbance Using Only One Controller Term

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Di-Yi Chen ◽  
Wei-Li Zhao ◽  
Xiao-Yi Ma ◽  
Run-Fan Zhang
Keyword(s):  
Chaos Control ◽  
Control Method ◽  
Sliding Mode ◽  
Chaotic Behavior ◽  
Coupled System ◽  
Noise Disturbance ◽  
Single Controller ◽  
Simulation Results ◽  
Control And Synchronization ◽  
Asymptotic Synchronization

This paper investigates the control and synchronization of the shunted nonlinear resistive-capacitive-inductance junction (RCLSJ) model under the condition of noise disturbance with only one single controller. Based on the sliding mode control method, the controller is designed to eliminate the chaotic behavior of Josephson junctions and realize the achievement of global asymptotic synchronization of coupled system. Numerical simulation results are presented to demonstrate the validity of the proposed method. The approach is simple and easy to implement and provides reference for chaos control and synchronization in relevant systems.

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