Resonant chaos control by periodic perturbations

Kraus, Mathias; Müller, Johannes; Lebender, D.; Schneider, F. W.

doi:10.1016/0009-2614(96)00884-6

Cited by 18 publications

(16 citation statements)

References 23 publications

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“…In a previous work [7], it has been shown that one of the infinite UPOs embedded in the chaotic attractor can be approached and stabilized by applying a small periodic perturbation to a system parameter or as an external force. Suppressing chaos in a low dimensional system by using a signal of resonant frequency has been confirmed analytically [8] and experimentally [9], and more applications can be found elsewhere, e.g., [10][11][12].…”

Section: A Chaos Control Methodsmentioning

confidence: 89%

“…For some high-speed systems such as chaotic circuits and fast electro-optical systems, there is difficulty in attaining real-time data of the system parameters and variables. In contrast to the feedback control techniques, the nonfeedback methods suppress chaotic motion by changing the system dynamics from a chaotic attractor to a periodic motion [7][8][9][10][11][12][13][14][15][16][17][18]. Relatively nonfeedback methods have the advantages in speed, flexibility, and no online monitoring and processing required.…”

Section: A Chaos Control Methodsmentioning

confidence: 99%

“…The nonfeedback methods include introduction of weak periodic parameter perturbation [7][8][9][10][11][12][13], constant force or bias [14], weak periodic pulses, open-loop entrainment control [15], and weak noise signals [16]. Comprehensive discussion of a variety of nonfeedback chaos control methods can be found in recent literature, e.g., Refs.…”

Section: A Chaos Control Methodsmentioning

confidence: 99%

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Controlling chaos with weak periodic signals optimized by a genetic algorithm

et al. 2004

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In the present study we develop a relatively novel and effective chaos control approach with a multimode periodic disturbance applied as a control signal and perform an in-depth analysis on this nonfeedback chaos control strategy. Different from previous chaos control schemes, the present method is of two characteristic features: (1) the parameters of the controlling signal are optimized by a genetic algorithm (GA) with the largest Lyapunov exponent used as an index of the stability, and (2) the optimization is justified by a fitness function defined with the target Lyapunov exponent and the controlling power. This novel method is then tested on the noted Rössler and Lorenz systems with and without the presence of noise. The results disclosed that, compared to the existing chaos control methods, the present GA-based control needs only significantly reduced signal power and a shorter transient stage to achieve the preset control goal. The switching control ability and the robustness of the proposed method for cases with sudden change in a system parameter and/or with the presence of noise environment are also demonstrated.

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Section: A Chaos Control Methodsmentioning

confidence: 89%

Section: A Chaos Control Methodsmentioning

confidence: 99%

Section: A Chaos Control Methodsmentioning

confidence: 99%

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Controlling chaos with weak periodic signals optimized by a genetic algorithm

et al. 2004

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“…General literature on this subject is extensive (see, e.g. [84] and references therein). In surface science, a good example illustrating this rule was presented by Ertl and co-workers [85] in their study of CO oxidation on the Pt(1 0 0) surface at UHV conditions.…”

Section: Temporal Perturbation Of Aperiodic Oscillationsmentioning

confidence: 99%

Periodic perturbation of the kinetics of heterogeneous catalytic reactions

Zhdanov

2004

Surface Science Reports

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“…Numerical simulation and experimental methods were reported in physical, chemical, and biological systems with major impact on many aspects of science and engineering [1][2][3][4][5][6][7][8][9][10]. A lot of theoretical and experimental work is dedicated to phase synchronized chaos [11][12][13][14][15][16] and also to lag synchronization [17].…”

Section: Introductionmentioning

confidence: 99%

Dynamic control by sinusoidal perturbation and by Gaussian noise of a system of two nonlinear oscillators: Computation and experimental results

2004

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In this paper we report numerical and experimental studies of the dynamic control of the inter-anode plasma of a double electrical discharge and of a system of two coupled nonlinear oscillators modeling this plasma. We compare the transition between chaotic dynamics and periodic dynamics induced by a sinusoidal perturbation and by small-dispersion Gaussian noise. Besides considerable differences between the effect of the two types of perturbation we also find important similarities. For small amplitude, both the sinusoidal and the white noise perturbations can induce the system to change from chaotic to regular dynamics. In the case of sinusoidal perturbation, the transition time from the chaotic to regular state has a definite duration that depends on the values of the perturbation parameters. The suppression of the perturbation has no influence on the state - the system remains in the same regular state. Subsequent reinstatement of the same type of perturbation with the same amplitude does not change the periodic state of the system but, for considerably higher amplitude, the system is switched back to its chaotic state. For moderate-amplitude sinusoidal perturbation, intermittent transitions between the chaotic and regular states is observed. Most of these predictions of the model have been observed experimentally in a system of two coupled electrical discharges. Our results suggest practical methods that can be used for controlling the discharge plasma dynamics.

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Resonant chaos control by periodic perturbations

Cited by 18 publications

References 23 publications

Controlling chaos with weak periodic signals optimized by a genetic algorithm

Controlling chaos with weak periodic signals optimized by a genetic algorithm

Periodic perturbation of the kinetics of heterogeneous catalytic reactions

Dynamic control by sinusoidal perturbation and by Gaussian noise of a system of two nonlinear oscillators: Computation and experimental results

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