Chaos Control and Synchronization

It is of vital importance to exactly estimate the unknown parameters of chaotic systems in chaos control and synchronization. In this paper, we present a method for estimating one-dimensional discrete chaotic system based on mean value method (MVM). It is proposed by exploiting the ergodic and synchronization features of chaos. It can effectively estimate the parameter value, and it is more exact than MVM. Finally, numerical simulations on Chebyshev map and Tent map show that the proposed method has better performance of parameter estimation than MVM.

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

International Journal of Numerical Methods for Heat &amp Fluid Flow ◽

10.1108/hff-03-2021-0211 ◽

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.

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Boundedness of a Class of Complex Lorenz Systems

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127421501017 ◽

2021 ◽

Vol 31 (07) ◽

pp. 2150101

Author(s):

Xu Zhang

Keyword(s):

Dynamical System ◽

Current Literature ◽

Chaos Control ◽

Type Systems ◽

Chaotic Attractors ◽

Strange Nonchaotic Attractors ◽

Control And Synchronization ◽

Ultimate Bound

The estimate of the ultimate bound for a dynamical system is an important problem, which is useful for chaos control and synchronization. In this paper, the estimated ultimate bound of a class of complex Lorenz systems is provided, which extends the parameter regions identified in the current literature on this problem. Based on these results, a kind of complex Lorenz-type systems is constructed, which might have many or infinitely many strange nonchaotic attractors, chaotic attractors, or an infinitely-many-scroll attractor.

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