Dynamic analysis and synchronization control of an unusual chaotic system with exponential term and coexisting attractors

Lai, Qiang; Akgül, Akif; Varan, Metin; Kengne, Jacques; Erguzel, Alper Turan

doi:10.1016/j.cjph.2018.09.015

Cited by 22 publications

(7 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A theoretical chaotic system's physical realizations are a practical way of giving its feasibility (Lai et al, 2018a;Rajagopal et al, 2018a;Akgul, 2017;Pehlivan et al, 2019;Ad iyaman et al, 2020). For this reason, we present the realization of a new hyperchaotic system by using common electronic components in this section.…”

Section: Circuit Design and Implementation Of The New Hyperchaotic Sy...mentioning

confidence: 99%

A new hyperchaotic system from T chaotic system: dynamical analysis, circuit implementation, control and synchronization

Emiroğlu

Akgül

Adıyaman

et al. 2021

View full text Add to dashboard Cite

Purpose The purpose of this paper is to develop new four-dimensional (4D) hyperchaotic system by adding another state variable and linear controller to three-dimensional T chaotic dynamical systems. Its dynamical analyses, circuit experiment, control and synchronization applications are presented. Design/methodology/approach A new 4D hyperchaotic attractor is achieved through a simulation, circuit experiment and mathematical analysis by obtaining the Lyapunov exponent spectrum, equilibrium, bifurcation, Poincaré maps and power spectrum. Moreover, hardware experimental measurements are performed and obtained results well validate the numerical simulations. Also, the passive control method is presented to make the new 4D hyperchaotic system stable at the zero equilibrium and synchronize the two identical new 4D hyperchaotic system with different initial conditions. Findings The passive controllers can stabilize the new 4D chaotic system around equilibrium point and provide the synchronization of new 4D chaotic systems with different initial conditions. The findings from Matlab simulations, circuit design simulations in computer and physical circuit experiment are consistent with each other in terms of comparison. Originality/value The 4D hyperchaotic system is presented, and dynamical analysis and numerical simulation of the new hyperchaotic system were firstly carried out. The circuit of new 4D hyperchaotic system is realized, and control and synchronization applications are performed.

show abstract

Section: Circuit Design and Implementation Of The New Hyperchaotic Sy...mentioning

confidence: 99%

A new hyperchaotic system from T chaotic system: dynamical analysis, circuit implementation, control and synchronization

Emiroğlu

Akgül

Adıyaman

et al. 2021

View full text Add to dashboard Cite

show abstract

“…where w := [ ] , u := [ 1 2 3 ] , 1 , 2 , and 3 are control inputs, and the subscript s denotes "slave." Define the synchronization error [54] as e fl w − w…”

Section: Problem Formulationmentioning

confidence: 99%

Exponential Synchronization of Chaotic Xian System Using Linear Feedback Control

et al. 2019

View full text Add to dashboard Cite

In this paper, a new linear feedback controller for synchronization of two identical chaotic systems in a master-slave configuration is presented. This controller requires knowing a priori Lipschitz constant of the nonlinear function of the chaotic system on its attractor. The controller development is based on an algebraic Riccati equation. If the gain matrix and the matrices of Riccati equation are selected in such a way that a unique positive definite solution is obtained for this equation, then, with respect to previous works, a stronger result can be guaranteed here: the exponential convergence to zero of the synchronization error. Additionally, the nonideal case is also studied, that is, when unmodeled dynamics and/or disturbances are present in both master system and slave system. On this new condition, the synchronization error does not converge to zero anymore. However, it is still possible to guarantee the exponential convergence to a bounded zone. Numerical simulation confirms the satisfactory performance of the suggested approach.

show abstract

“…Chaos-based applications is a hot topic in science and engineering. Oscillators 5 , steganography 6 , synchronization 7 , control 8 , and parameter estimation have all employed chaotic systems. Some chaotic systems have a unique feature.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of chaotic system based on circuit design with Ulam stability through fractal-fractional derivative with power law kernel

Khan

Ahmad

Shah

et al. 2023

Sci Rep

View full text Add to dashboard Cite

In this paper, the newly developed Fractal-Fractional derivative with power law kernel is used to analyse the dynamics of chaotic system based on a circuit design. The problem is modelled in terms of classical order nonlinear, coupled ordinary differential equations which is then generalized through Fractal-Fractional derivative with power law kernel. Furthermore, several theoretical analyses such as model equilibria, existence, uniqueness, and Ulam stability of the system have been calculated. The highly non-linear fractal-fractional order system is then analyzed through a numerical technique using the MATLAB software. The graphical solutions are portrayed in two dimensional graphs and three dimensional phase portraits and explained in detail in the discussion section while some concluding remarks have been drawn from the current study. It is worth noting that fractal-fractional differential operators can fastly converge the dynamics of chaotic system to its static equilibrium by adjusting the fractal and fractional parameters.

show abstract

Dynamic analysis and synchronization control of an unusual chaotic system with exponential term and coexisting attractors

Cited by 22 publications

References 29 publications

A new hyperchaotic system from T chaotic system: dynamical analysis, circuit implementation, control and synchronization

A new hyperchaotic system from T chaotic system: dynamical analysis, circuit implementation, control and synchronization

Exponential Synchronization of Chaotic Xian System Using Linear Feedback Control

Dynamics of chaotic system based on circuit design with Ulam stability through fractal-fractional derivative with power law kernel

Contact Info

Product

Resources

About