Browsing by Author "Vladimir S. Zykov"

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    Instabilities of the resonance attractor for spiral waves in an excitable medium
    (2002-01-01) Vladimir S. Zykov; On Uma Kheowan; Orapin Rangsiman; Stefan C. Müller; Otto von Guericke University of Magdeburg; Mahidol University
    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. © 2002 The American Physical Society.
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    Measurements of kinematical parameters of spiral waves in media of low excitability
    (2001-01-01) On Uma Kheowan; Vilmos Gáspár; Vladimir S. Zykov; Stefan C. Müller; Otto von Guericke University of Magdeburg; Debreceni Egyetem Termeszettudomanyi es Technologiai Kar; Mahidol University
    The dynamics of spiral waves rotating in a thin layer of the light sensitive Belousov-Zhabotinsky reaction mixture are studied under a homogeneous and steady illumination. At a given composition of the excitable medium, the spiral waves meand, when no or low intensity light is applied, or rigidly rotate, when the light intensity is increased sufficiently. There exists, however, a critical value of light intensity above which no wave activity is supported by the medium, since its excitability is too strongly reduced by the illumination. In the vicinity of this critical value the basic kinematical parameters of rigidly rotating spirals (such as the rotation period, wavelength, propagation velocity, and the diameter of the spiral core) are measured as a function of the illumination intensity. The experimental observations are in good agreement with the predictions based on an earlier proposed kinematical theory of spiral waves in media of low excitability.
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    Spiral wave dynamics under feedback derived from a confined circular domain
    (2001-01-01) On Uma Kheowan; Chi Keung Chan; Vladimir S. Zykov; Orapin Rangsiman; Stefan C. Müller; Otto von Guericke University of Magdeburg; Mahidol University; Academia Sinica Taiwan
    Spiral waves are induced in a thin layer of the light-sensitive Belousov-Zhabotinsky reaction and controlled by a time-dependent uniform illumination. The intensity of the illumination is taken to be proportional to the average wave activity observed within a circular domain of the reaction layer. Stabilization and destabilization of spiral waves, as well as the existence of additional types of attractors, are demonstrated. A simple mathematical description is proposed in order to explain the existence of the attractors and the dependence of their size on the time delay in the feedback loop. © 2001 The American Physical Society.
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    Transitions between orbits of resonance attractors for spiral waves
    (2001-03-05) On Uma Kheowan; Vladimir S. Zykov; Orapin Rangsiman; Stefan C. Müller; Otto von Guericke University of Magdeburg; Mahidol University
    The detailed structure of the resonance attractor in the Belousov-Zhabotinsky (BZ) system was experimentally studied. In particular, the role of the parameters in the feedback loop and the initial location of the spiral wave for the size of the stationary orbit was systematically examined. Finally, the dynamics of the spiral wave under variation of the parameters in the feedback loop during the experiment was analyzed.