Periodic entrainment of chaotic logistic map dynamics

Jackson, E. Atlee; Hu, Ang

doi:10.1016/0167-2789(90)90155-i

Cited by 110 publications

(21 citation statements)

References 2 publications

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“…The chaos represents an interesting topic because irregular oscillations can be undesirable in some physical systems. Control and synchronization schemes for different chaotic systems have been explored by various researchers since long [1][2][3][4][5][6][7][8]. These systems find applications in spread spectrum waveforms, secure communication, cryptography and they are utilized as chaotic sources in transmitter-receiver schemes [9][10][11][12][13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Observer-based synchronization scheme for a class of chaotic systems using contraction theory

Sharma

Kar

2010

Nonlinear Dyn

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In this paper, an adaptive synchronization scheme is proposed for a class of nonlinear systems. The design utilizes an adaptive observer, which is quite useful in establishing a transmitter-receiver kind of synchronization scheme. The proposed approach is based on contraction theory and provides a very simple way of establishing exponential convergence of observer states to actual system states. The class of systems addressed here has uncertain parameters, associated with the part of system dynamics that is a function of measurable output only. The explicit conditions for the stability of the observer are derived in terms of gain selection of the observer. Initially, the case without uncertainty is considered and then the results are extended to the case with uncertainty in parameters of the system. An application of the proposed approach is presented to synchronize the family of N chaotic systems which are coupled through the output variable only. The numerical results are presented for designing an adaptive observer for the chaotic Chua system to verify the efficacy of the proposed approach. Explicit bounds on observer gains are derived by exploiting the properties of the chaotic attractor exhibited by Chua's system. Convergence of uncertain parameters is also analyzed for this case and numerical simulations depict the convergence of parameter estimates to their true value.

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Section: Introductionmentioning

confidence: 99%

Observer-based synchronization scheme for a class of chaotic systems using contraction theory

Sharma

Kar

2010

Nonlinear Dyn

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“…In recent years there has been a great deal of research related to entrainment and migration control methods, proposed by Jackson (1990Jackson ( , 1991a , Plapp and Hu È bler (1990) , Jackson and Hu È bler (1990) , Jackson and Kodogeorgiou (1992) and Jackson and Grosu (1995) . This general approach has been successfully applied to many complex dynamic systems (Chen and Dong 1993) such as multi-attractor systems (Jackson 1991a) , multiperiodic forcing control of a one-dimensional logistic map (Jackson 1990), a Gaussian-related map (Jackson 1991a) , and the two-dimensional He Â non and Ikeda map (Jackson and Kodogeorgiou 1992).…”

Section: Introductionmentioning

confidence: 99%

A global control of polynomial chaotic systems

Wang¹,

Wang²

1999

International Journal of Control

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“…(0.1). In many cases this solution is a stable solution with a large basin of attraction [6]. If the initial conditions lie within the basin of attraction, the driving force given by Eq.…”

Section: General Resonance Spectroscopymentioning

confidence: 99%