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.
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
\Bibitem{TsyBik09}
\by M.~A.~Tsyganov, V.~N.~Biktashev
\paper Soliton and half-soliton interaction of solitary waves in excitable media
with non-linear cross-diffusion
\jour Computer Research and Modeling
\yr 2009
\vol 1
\issue 1
\pages 109--115
\mathnet{http://mi.mathnet.ru/crm628}
\crossref{https://doi.org/10.20537/2076-7633-2009-1-1-109-115}
Linking options:
https://www.mathnet.ru/eng/crm628
https://www.mathnet.ru/eng/crm/v1/i1/p109
This publication is cited in the following 1 articles:
E. E. Giricheva, “Vliyanie napravlennykh peremeschenii khischnika na formirovanie prostranstvennykh struktur v modeli trekhvidovogo soobschestva s uchetom vseyadnosti khischnika”, Kompyuternye issledovaniya i modelirovanie, 15:6 (2023), 1617–1634
Citation in format AMSBIB
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