Review article on adaptive synchronization of chaotic systems with unknown parameters

Adloo, Hassan; Roopaei, Mehdi

doi:10.1007/s11071-010-9880-6

Cited by 35 publications

(14 citation statements)

References 26 publications

(80 reference statements)

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“…Remark 3: The classical system like Lorenz system and lü system can be synchronized via adaptive method with single controller. Do not need to construct multiple controllers like the literature [20].…”

Section: E P E E Q Ementioning

confidence: 99%

“…References therein [19] achieved synchronous control of Chua's circuit based on the symbol function. Synchronization of chaotic systems with unknown parameters was investigated by utilizing adaptive method [20], and passive synchronization control, backstepping method [21]- [23], and so on. However, during the above employed approaches, controllers are designed more than one, which will be difficult in industrial implementation and cost control in the future.…”

Section: Introductionmentioning

confidence: 99%

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A New Three-Dimensional Chaotic System with Constant Exponent Spectrum: Analysis, Synchronization and Circuit Implementation

Jiang¹,

Wu²

2016

JSW

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Abstract:A new chaotic system with constant Lyapunov exponent spectrum is presented, two system parameters of which remain constant exponent characteristics. The basic dynamic properties of the new system are analyzed by Poincar section, Lyapunov exponent and dimension and the signal power spectrum. Based on the Lyapunov exponent spectrum, bifurcation diagrams and state variable amplitude with respect to system parameters show that the new system has two parameters with globally nonlinear modulation characteristic. Based on the Lyapunov stability theory and the improvement of the traditional method, through constructing a Lyapunov function with containing a positive constant that the complete synchronization with single controllers are achieved by means of nonlinear active feedback, adaptive, backstepping and passive control theory, respectively. And the designed single controllers are verified via numerical simulation. Because of single controller, synchronous switch circuit consists of four synchronization schemes is implemented, which further validate the correctness and practicability of the single controllers.

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Section: E P E E Q Ementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A New Three-Dimensional Chaotic System with Constant Exponent Spectrum: Analysis, Synchronization and Circuit Implementation

Jiang¹,

Wu²

2016

JSW

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“…or may be time varying and/or inaccessible to direct measurements. Therefore, the synchronization of two uncertain chaotic systems is essential [37][38][39][40][41][42].…”

Section: Synchronization Studymentioning

confidence: 99%

“…Obviously, this perfect synchronization may be exploited in secure communication using the technique of parameter modulation/estimation [37][38][39] as the system can be designed and implemented at any given frequency band depending on the values of circuit components.…”

Section: Numerical Verificationmentioning

confidence: 99%

Theoretical Analysis and Adaptive Synchronization of a 4D Hyperchaotic Oscillator

2014

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We propose a new mathematical model of the TNC oscillator and study its impact on the dynamical properties of the oscillator subjected to an exponential nonlinearity. We establish the existence of hyperchaotic behavior in the system through theoretical analysis and by exploiting electronic circuit experiments. The obtained numerical results are found to be in good agreement with experimental observations. Moreover, the new technique on adaptive control theory is used on our model and it is rigorously proven that the adaptive synchronization can be achieved for hyperchaotic systems with uncertain parameters.

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“…This control method differs from other control methods because it does not require advance information about the limits on these uncertain or time-varying parameters because it relates to a control law that changes itself. Recently, many papers are available on synchronization of chaotic systems using this method of control [20][21][22][23][24][25][26][27][28][29][30][31]. This paper is organized as follows: The second section deal with the description and some properties of the novel chaotic system.…”

Section: Introductionmentioning

confidence: 99%

Analysis, dynamics and adaptive control synchronization of a novel chaotic 3-D system

Hannachi

2019

SN Appl. Sci.

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In this paper, a new 3D chaotic dissipative system is introduced. Basics dynamical characteristics and properties are studied such as equilibrium points, Lyapunov exponent spectrum, Kaplan-Yorke dimension. Dynamics of the new 3D chaotic system is investigated also numerically using largest Lyapunov exponents spectrum and bifurcation diagrams. We derive new control results via adaptive control method based on Lyapunov stability theory and adaptive control theory for globally and exponentially synchronizing the identical 3-D novel chaotic systems with unknown system parameters. The results are validated by numerical simulation using Matlab.

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Review article on adaptive synchronization of chaotic systems with unknown parameters

Cited by 35 publications

References 26 publications

A New Three-Dimensional Chaotic System with Constant Exponent Spectrum: Analysis, Synchronization and Circuit Implementation

A New Three-Dimensional Chaotic System with Constant Exponent Spectrum: Analysis, Synchronization and Circuit Implementation

Theoretical Analysis and Adaptive Synchronization of a 4D Hyperchaotic Oscillator

Analysis, dynamics and adaptive control synchronization of a novel chaotic 3-D system

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