Passive and impulsive synchronization of a new four-dimensional chaotic system

Hamiche, Hamid; Kemih, Karim; Ghanes, Malek; Zhang, Gang; Djennoune, Saïd

doi:10.1016/j.na.2010.09.051

Cited by 15 publications

(6 citation statements)

References 18 publications

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“…x + e 2 y + e 2 z and Figure 7 demonstrates the time history of the synchronization state variables of the MS (Equation 8) and DS (Equation 9) systems, which are (x 1 , x 2 ), (y 1 , y 2 ), and (z 1 , z 2 ) at time t = 0 control signals are activated. Moreover, Figure 8 illustrates the action control's response time from Equation (20) to achieve chaos synchronization between the Master-Drive system. Controllers modify inputs to set the system's output to the desired results.…”

Section: Simulation and Resultsmentioning

confidence: 99%

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Shimizu–Morioka's chaos synchronization: An efficacy analysis of active control and backstepping methods

Tarammim

Akter

2023

Front. Appl. Math. Stat.

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This research study inspects the effectiveness of synchronization methods such as active control and backstepping control from systematic design procedures of a synchronized Shimizu–Morioka system for the same parameter. It aimed to achieve synchronization between the state variables of two identical Shimizu–Morioka chaotic systems by defining the proposed varieties of the error dynamics coefficient matrix. Furthermore, this study also aimed to designed an active controller that enables the synchronization of these systems. The use of designed recursive backstepping nonlinear controllers was based on the Lyapunov function. Furthermore, it also demonstrated the stability of the synchronization of the nonlinear identical Shimizu–Morioka system. The new virtual state variable and establishment of Lyapunov functionals are used in the backstepping controller to stabilize and reduce errors between the Master (MS)/Drive (DS) systems. For comparison, the complexity of active controllers is verified to be such that the designed controller's effectiveness based on backstepping is attainable in engineering applications. Finally, numerical simulations are performed to demonstrate the effectiveness of the proposed synchronization strategy with the Runge–Kutta (RK-4) algorithm of fourth order through MatLab Simulink.

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Section: Simulation and Resultsmentioning

confidence: 99%

“…These characteristics are critical in trouble as chaotic systems cannot be globally synchronized. However, a nonlinear system that exhibits chaotic behavior may follow unintended trajectories, thus one of the leading research areas for the nonlinear system deals with how to control chaotic systems [20].…”

Section: Introductionmentioning

confidence: 99%

Shimizu–Morioka's chaos synchronization: An efficacy analysis of active control and backstepping methods

Tarammim

Akter

2023

Front. Appl. Math. Stat.

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“…This interest is increased by practical applications in different fields, particularly in secure/private communications [3][4][5]. Many different methods have been presented for the synchronization of chaotic systems with linear or nonlinear feedback control [6,7], adaptive control [8], passive control [9], impulsive control [10] or observer approach [11]. Due to its great potential in secure/private communications domain, the generation of hyperchaos has recently become a focal topic for research [12,13].…”

Section: Introductionmentioning

confidence: 99%

Analysis and implementation of a novel robust transmission scheme for private digital communications using Arduino Uno board

Hamiche¹,

Guermah²,

Saddaoui

et al. 2015

Nonlinear Dyn

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In this paper, we present a new scheme for the secured transmission of discrete information based on hyperchaotic discrete dynamics. The system is a modified-Henon hyperchaotic discrete-time oscillator considered as transmitter and a delayed step-by-step observer used as receiver. The transmitter parameters play the role of secret keys of the transmission scheme. To increase the robustness of the secure data transmission against known plain-text attacks, the message to be sent is encrypted by additional secret keys and inserted by inclusion method in the chaotic discrete-time system dynamics. By this way, the parameters used as secret keys cannot be identified with usual techniques. Simulation results are presented to highlight the performances of the proposed method. One of the main contributions of this paper is to demonstrate the feasibility of discrete realization of a chaotic observer-based secured transmission scheme. Indeed, experimental implementation results using Arduino Uno board validate the proposed approach, since it exhibits good performances of throughput and cost in terms of resources used.

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“…In recent years, because of its important application value in signal processing, secure communication and other fields, chaos synchronization has become one of the major problems in mathematics and engineering. A large number of effective synchronization methods have been proposed [3][4][5][6][7][8][9][10][11]. The amount of theories as well as that of experiments and applications grows very fast in this research direction.…”

Section: Introductionmentioning

confidence: 99%

Synchronization of Chua's circuits based on strictly positive realness

Niu

Zhang

Wang

2014

The 26th Chinese Control and Decision Conference (2014 CCDC)

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The purpose of this paper is to verify that the method proposed in [1] is still feasible when the nonlinear terms of the error system are some piecewise linear functions containing explicit error state variables. The synchronization of Chua's circuits is considered as an example to illustrate the validity of the method. With the aid of the stability estimation and some numerical simulation results, the feasibility and effectiveness of this method can be proven. Moreover, the synchronization controller can still be designed without considering either the chaos ranges of the variables or the variable coefficients and structures of the nonlinear terms.

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Passive and impulsive synchronization of a new four-dimensional chaotic system

Cited by 15 publications

References 18 publications

Shimizu–Morioka's chaos synchronization: An efficacy analysis of active control and backstepping methods

Shimizu–Morioka's chaos synchronization: An efficacy analysis of active control and backstepping methods

Analysis and implementation of a novel robust transmission scheme for private digital communications using Arduino Uno board

Synchronization of Chua's circuits based on strictly positive realness

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