Beyond the Kuramoto-Zel’dovich theory: Steadily rotating concave spiral waves and their relation to the echo phenomenon |
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Authors: | O. A. Mornev I. M. Tsyganov O. V. Aslanidi M. A. Tsyganov |
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Affiliation: | (1) Institute of Theoretical and Experimental Biophysics, Russian Academy of Sciences, pr. Nauki, Pushchino, Moscow region, 142292, Russia;(2) Moscow State University, Vorob’evy gory, Moscow, 119899, Russia;(3) Institute of Cell Biophysics, Russian Academy of Sciences, Pushchino, Moscow region, 142292, Russia;(4) School of Biomedical Sciences, University of Leeds, Leeds, LS2 9JT, UK |
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Abstract: | In numerical experiments with the Fitzhugh-Nagumo set of reaction-diffusion equations describing two-dimensional excitable media, unusual solutions are found that correspond to a concave spiral wave steadily rotating round a circular obstacle in a finite-size medium. Such a wave arises in the region of parameters corresponding to the solitonlike regime (see text); it appears due to the interaction between the peripheral areas of a “seed” spiral wave with a convex front and the echo waves incoming from the outer boundaries of a medium. The solutions obtained are in contradiction with intuition and represent a numerical counterexample to the known theories that forbid steadily moving excitation waves with concave fronts. Nevertheless, a concave spiral wave is a stable object; being transformed to the usual spiral wave with a convex front by suppressing echo at the outer boundaries of the medium, it is again recovered upon restoring the echo conditions. In addition to the single-arm spiral concave wave, solutions are obtained that describe multiarm waves of this type; for this reason, the concave fronts of these waves are a coarse property. |
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