Circuit realization, chaos synchronization and estimation of parameters of a hyperchaotic system with unknown parameters

Elsonbaty, Amr; Elsaid, A.; Nour, H. M.

doi:10.1016/j.joems.2013.11.007

Cited by 15 publications

(7 citation statements)

References 12 publications

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“…Then, in [55], a novel control approach does the synchronization of two non-identical 4-D hyperchaotic systems. Finally, in [56,57], the synchronization of two novel hyperchaotic system with unknown parameters and the circuit realization, control and synchronization of a novel hyperchaotic system are presented, respectively. This study considers the discovery of a novel chaotic system, as well as the homoclinic and heteroclinic chaotic properties of this type of system.…”

Section: Related Workmentioning

confidence: 99%

Robust Stabilization and Synchronization of a Novel Chaotic System with Input Saturation Constraints

Azar

Serrano

Zhu

et al. 2021

Entropy

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In this paper, the robust stabilization and synchronization of a novel chaotic system are presented. First, a novel chaotic system is presented in which this system is realized by implementing a sigmoidal function to generate the chaotic behavior of this analyzed system. A bifurcation analysis is provided in which by varying three parameters of this chaotic system, the respective bifurcations plots are generated and evinced to analyze and verify when this system is in the stability region or in a chaotic regimen. Then, a robust controller is designed to drive the system variables from the chaotic regimen to stability so that these variables reach the equilibrium point in finite time. The robust controller is obtained by selecting an appropriate robust control Lyapunov function to obtain the resulting control law. For synchronization purposes, the novel chaotic system designed in this study is used as a drive and response system, considering that the error variable is implemented in a robust control Lyapunov function to drive this error variable to zero in finite time. In the control law design for stabilization and synchronization purposes, an extra state is provided to ensure that the saturated input sector condition must be mathematically tractable. A numerical experiment and simulation results are evinced, along with the respective discussion and conclusion.

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Section: Related Workmentioning

confidence: 99%

Robust Stabilization and Synchronization of a Novel Chaotic System with Input Saturation Constraints

Azar

Serrano

Zhu

et al. 2021

Entropy

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“…228987x 1 y 1 z 1 188295:5x 1 y 1 w 1 + 208642x 1 z 1 w 1 + 310644:7y 1 z 1 w 1 : g 4 = 12:7 x 1 4130 y 1 + 4943:28 z 1 + 3311 w 1 + 240:4x 3 1 + 77548:9y…”

Section: 1unclassified

“…Thus, the hyperchaotic systems have higher unpredictability and more randomness than simple chaotic systems. Some of the applications of dynamical systems and chaos involve mathematical biology, …nancial systems, chaos control, synchronization, electronic circuits, and neuroscience research, while hyperchaotic systems are preferred in many applications including secure communications, chaos based image encryption, and cryptography [3]- [23].…”

Section: Introductionmentioning

confidence: 99%

DYNAMICAL BEHAVIORS OF A NEW HYPERCHAOTIC SYSTEM WITH ONE NONLINEAR TERM Vol. 3(1) Jan 2015, No. 1, pp. 1-18 A.M.A. EL-SAYED, H.M. NOUR, A. ELSAID, A. ELSONBATY

2015

Electronic Journal of Mathematical Analysis and Applications

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This paper is devoted to introduce a novel hyperchaotic system with only one nonlinear term. Existence and uniqueness of the solution of the proposed system are studied. Continuous dependence on initial conditions of the system's solution and stability of system's equilibrium points are investigated. Dynamical behaviors are explored via theoretical analysis, bifurcation diagrams, and phase portraits of the new system. Finally, a circuit implementation of the novel hyperchaotic system is proposed.

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“…After the remarkable work [1], chaos synchronization has been widely investigated in the relevant literature [2][3][4]. At present, chaos synchronization has received increasing interest in many scientific disciplines, such as chemical processes and biological systems [5], cryptosystem [6], information processing [7], secure communications [8], and many physical systems [9]. As a result, a variety of control methods and techniques have been developed to study the chaos synchronization.…”

Section: Introductionmentioning

confidence: 99%

“…As a result, a variety of control methods and techniques have been developed to study the chaos synchronization. These include the adaptive control strategy [9], projective synchronization [10], sliding mode control [11], nonlinear control techniques [12], and active control method [13], which are well-known synchronization control techniques among others. Among these techniques, the active control (AC) and adaptive synchronization control (ASC) strategies have attracted a great interest in the literature concerned because of their easy implementation to practical systems [14][15][16][17][18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Controller Parameter Optimization for the Robust Synchronization of Chaotic Systems with Known and Unknown Parameters

Ahmad

Saaban

Ibrahim

2017

J. Uncertain. Anal. Appl.

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In this paper, a synchronization problem of a three-dimensional (3-D) Coullete chaotic system using the active-and adaptive-based synchronization control techniques is addressed. Based on the Routh-Hurwitz criterion and using the active control algorithm, a single control function is considered and a computational study is performed to identify the correct balance between the converging rates of the synchronization error signals to the origin and magnitude of the linear controlling parameters (LCPs) for the globally exponential synchronization (GES) between two identical 3-D Coullete chaotic systems. In order to achieve the complete synchronization (CS) objective with unknown model uncertainties, external disturbances, and unknown time-varying parameters, a novel nonlinear adaptive synchronous controller is proposed and suitable adaptive laws of time-varying parameters are designed that accomplish the asymptotic synchronization between two identical uncertain 3-D Coullete chaotic systems. The two synchronizing controlling approaches are applied to investigate the CS phenomenon, and the results are compared. Open research problems are also discussed. All simulations results are carried out to validate the effectiveness of the proposed synchronization control approaches by using Mathematica 10.0.

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Circuit realization, chaos synchronization and estimation of parameters of a hyperchaotic system with unknown parameters

Cited by 15 publications

References 12 publications

Robust Stabilization and Synchronization of a Novel Chaotic System with Input Saturation Constraints

Robust Stabilization and Synchronization of a Novel Chaotic System with Input Saturation Constraints

DYNAMICAL BEHAVIORS OF A NEW HYPERCHAOTIC SYSTEM WITH ONE NONLINEAR TERM Vol. 3(1) Jan 2015, No. 1, pp. 1-18 A.M.A. EL-SAYED, H.M. NOUR, A. ELSAID, A. ELSONBATY

Controller Parameter Optimization for the Robust Synchronization of Chaotic Systems with Known and Unknown Parameters

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