|
Pis'ma v Zhurnal Èksperimental'noi i Teoreticheskoi Fiziki, 2003, Volume 77, Issue 6, Pages 319–325
(Mi jetpl2759)
|
|
|
|
This article is cited in 11 scientific papers (total in 11 papers)
PLASMA, GASES
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.
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.
Received: 27.11.2002 Revised: 12.02.2003
Citation:
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
Linking options:
https://www.mathnet.ru/eng/jetpl2759 https://www.mathnet.ru/eng/jetpl/v77/i6/p319
|
|