Instabilities of the resonance attractor for spiral waves in an excitable medium

Vladimir S. Zykov; On Uma Kheowan; Orapin Rangsiman; Stefan C. Müller

doi:10.1103/PhysRevE.65.026206

Instabilities of the resonance attractor for spiral waves in an excitable medium

Vladimir S. Zykov
, On Uma Kheowan
, Orapin Rangsiman
, Stefan C. Müller

Department of Chemistry

Otto-von-Guericke-Universität Magdeburg
Mahidol University

Research output: Contribution to journal › Article › peer-review

27 Citations (Scopus)

Abstract

During an experimental study of the resonance attractor for spiral waves in the light-sensitive Belousov-Zhabotinsky reaction, strong deviations of the attractor trajectories from circular orbits are observed if the time delay in the feedback loop becomes relatively long. A theory is developed that reduces the spiral wave dynamics under a long-delayed control to a higher order iterative map. Then the observed deviations are explained to be a result of instabilities appearing due to the Neimark bifurcation of the map. The theoretical predictions are in good agreement with the experimental data.

Original language	English
Journal	Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume	65
Issue number	2
DOIs	https://doi.org/10.1103/PhysRevE.65.026206
Publication status	Published - 2002

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10.1103/PhysRevE.65.026206

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abstract = "During an experimental study of the resonance attractor for spiral waves in the light-sensitive Belousov-Zhabotinsky reaction, strong deviations of the attractor trajectories from circular orbits are observed if the time delay in the feedback loop becomes relatively long. A theory is developed that reduces the spiral wave dynamics under a long-delayed control to a higher order iterative map. Then the observed deviations are explained to be a result of instabilities appearing due to the Neimark bifurcation of the map. The theoretical predictions are in good agreement with the experimental data.",

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AU - Zykov, Vladimir S.

AU - Kheowan, On Uma

AU - Rangsiman, Orapin

AU - Müller, Stefan C.

PY - 2002

Y1 - 2002

N2 - During an experimental study of the resonance attractor for spiral waves in the light-sensitive Belousov-Zhabotinsky reaction, strong deviations of the attractor trajectories from circular orbits are observed if the time delay in the feedback loop becomes relatively long. A theory is developed that reduces the spiral wave dynamics under a long-delayed control to a higher order iterative map. Then the observed deviations are explained to be a result of instabilities appearing due to the Neimark bifurcation of the map. The theoretical predictions are in good agreement with the experimental data.

AB - During an experimental study of the resonance attractor for spiral waves in the light-sensitive Belousov-Zhabotinsky reaction, strong deviations of the attractor trajectories from circular orbits are observed if the time delay in the feedback loop becomes relatively long. A theory is developed that reduces the spiral wave dynamics under a long-delayed control to a higher order iterative map. Then the observed deviations are explained to be a result of instabilities appearing due to the Neimark bifurcation of the map. The theoretical predictions are in good agreement with the experimental data.

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ER -

Instabilities of the resonance attractor for spiral waves in an excitable medium

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