This article is cited in 3 scientific papers (total in 3 papers)
Beyond the Kuramoto-Zel'dovich theory: Steadily rotating concave spiral waves and their relation to the echo phenomenon
O. A. Morneva, I. M. Tsyganovb, O. V. Aslanidicd, M. A. Tsyganova
a Institute for Theoretical and Experimental Biophysics, Russian Academy of Sciences, Pushino, Moscow region
b M. V. Lomonosov Moscow State University
c School of Biomedical Sciences, University of Leeds
d Institute of Cell Biophysics, Russian Academy of Sciences, Pushchino, Moskovskaya obl.
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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Journal of Experimental and Theoretical Physics Letters, 2003, 77:6, 270–275
03.40.Kf, 52.35.Sb, 87.22.Jb,
O. A. Mornev, I. M. Tsyganov, O. V. Aslanidi, M. A. Tsyganov, “Beyond the Kuramoto-Zel'dovich theory: Steadily rotating concave spiral waves and their relation to the echo phenomenon”, Pis'ma v Zh. Èksper. Teoret. Fiz., 77:6 (2003), 319–325; JETP Letters, 77:6 (2003), 270–275
Citation in format AMSBIB
\by O.~A.~Mornev, I.~M.~Tsyganov, O.~V.~Aslanidi, M.~A.~Tsyganov
\paper Beyond the Kuramoto-Zel'dovich theory: Steadily rotating concave spiral waves and their relation to the echo phenomenon
\jour Pis'ma v Zh. \`Eksper. Teoret. Fiz.
\jour JETP Letters
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