Stabilization of chaos by proportional pulses in the system variables

Matías, Manuel A.; Güémez, J.

doi:10.1103/physrevlett.72.1455

Cited by 105 publications

(39 citation statements)

References 20 publications

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“…While synchronization deals basically with the difference between the dynamics of the two subsystems, here we are also interested in the attractor on which the two subsystems get synchronized. They are many ways to couple two dynamical systems 19 and the scheme that we have used here enter in the family of the so-called diffusive coupling. Diffusion is not always symmetric, for example, if the diffusion parameter is not constant 20 or if it exists an asymmetry due to some constraint as, for example, in physiological membranes that selectively diffuse the ions.…”

Section: A Roessler In the Not Funnel Regimementioning

confidence: 99%

Chaos suppression through asymmetric coupling

Bragard

Vidal

Mancini

et al. 2007

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We study pairs of identical coupled chaotic oscillators. In particular, we have used Roessler ͑in the funnel and no funnel regimes͒, Lorenz, and four-dimensional chaotic Lotka-Volterra models. In all four of these cases, a pair of identical oscillators is asymmetrically coupled. The main result of the numerical simulations is that in all cases, specific values of coupling strength and asymmetry exist that render the two oscillators periodic and synchronized. The values of the coupling strength for which this phenomenon occurs is well below the previously known value for complete synchronization. We have found that this behavior exists for all the chaotic oscillators that we have used in the analysis. We postulate that this behavior is presumably generic to all chaotic oscillators. In order to complete the study, we have tested the robustness of this phenomenon of chaos suppression versus the addition of some Gaussian noise. We found that chaos suppression is robust for the addition of finite noise level. Finally, we propose some extension to this research. © 2007 American Institute of Physics. ͓DOI: 10.1063/1.2797378͔Chaos suppression has been realized in the past by using techniques related to parameter perturbations as well parametric forcings. In the present paper, we introduce a new technique based on couplings. Here the recipe rests on selecting an adequate coupling able to drive a chaotic dynamics towards a regular periodic attractor.

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Section: A Roessler In the Not Funnel Regimementioning

confidence: 99%

Chaos suppression through asymmetric coupling

Bragard

Vidal

Mancini

et al. 2007

Chaos: An Interdisciplinary Journal of Nonlinear Science

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show abstract

“…OGY method has been applied to many practical systems, and some extensions of this method have been proposed [15,16]. Since a number of presented methods modiÿes the control parameters once each period of PoincarÃ e map [14][15][16][17], the stabilization can be realized only for such periodic orbits whose maximal Lyapunov exponent is smaller than the reciprocal of the time interval between parameter changes. The uctuation noise leads to occasional bursts of the system into the region far from the desired periodic orbit, and these bursts are more frequent for a large noise.…”

Section: Introductionmentioning

confidence: 99%

Chaotic attitude motion and its control of spacecraft in elliptic orbit and geomagnetic field

Liu

Chen

2004

Acta Astronautica

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“…In [12,15], the authors introduced a specific method to have control over chaos. In discrete dynamics, the authors applied instantaneous pulses on the system variables ܺ , once every ‫‬ iterations, in the form ܺ ൌ ݇ܺ ( i is a multiple of ‫)‬…”

Section: The Periodic Proportional Pulse Methods To Control Chaos In Tmentioning

confidence: 99%

Chaotic behavior and its control in a two parameter map with variable Jacobian

Sarmah¹,

Paul²

2013

IJSEA

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Inthe present paper we have considered the mapwhere , are parameters. The map was originally proposed by Maynard Smith [17] for study of population growth. We have shown how chaos creep into the model. We have used the techniques of Lyapunov exponent, time series analysis, Fourier spectra, Bifurcation diagram, correlation and embedding dimension etc. to draw our conclusions. Further, we have shown how the 'periodic proportional pulse' method can be used to control the chaos generated in the system.

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Stabilization of chaos by proportional pulses in the system variables

Cited by 105 publications

References 20 publications

Chaos suppression through asymmetric coupling

Chaos suppression through asymmetric coupling

Chaotic attitude motion and its control of spacecraft in elliptic orbit and geomagnetic field

Chaotic behavior and its control in a two parameter map with variable Jacobian

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