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This article is cited in 1 scientific paper (total in 1 paper)
ANALYSIS AND MODELING OF COMPLEX LIVING SYSTEMS
Soliton and half-soliton interaction of solitary waves in excitable media
with non-linear cross-diffusion
M. A. Tsyganova, V. N. Biktashevb a Institute of Theoretical and Experimental Biophysics, Institutskaya str. 3, Puschino, Moscow Region, 142290, Russia
b University of Liverpool, Department of Mathematical Sciences, Mathematical Sciences Building, Liverpool L69 7ZL ,England, U. K.
Abstract:
We have studied properties of non-linear waves in a mathematical model of a predator–prey system with taxis. We demonstrate that, for systems with negative and positive taxis there typically exists a large region in the parameter space, where the waves demonstrate quasi-soliton interaction; colliding waves can penetrate through each other, and waves can also reflect from impermeable boundaries. In this paper, we use numerical simulations to demonstrate also a new wave phenomenon — a half-soliton interaction of waves, when of two colliding waves, one annihilates and the other continues to propagate. We show that this effect depends on the “ages” or, equivalently, “widths” of the colliding waves.
Keywords:
soliton, wave propagation, predator–prey system, cross-diffusion.
Received: 25.10.2008
Citation:
M. A. Tsyganov, V. N. Biktashev, “Soliton and half-soliton interaction of solitary waves in excitable media
with non-linear cross-diffusion”, Computer Research and Modeling, 1:1 (2009), 109–115
Linking options:
https://www.mathnet.ru/eng/crm628 https://www.mathnet.ru/eng/crm/v1/i1/p109
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