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Zbl 1080.35036
Biktashev, V.N.; Brindley, J.; Holden, A.V.; Tsyganov, M.A.
Pursuit-evasion predator-prey waves in two spatial dimensions. (English)
[J] Chaos 14, No. 4, 988-994 (2004). ISSN 1054-1500; ISSN 1089-7682/e

Summary: We consider a spatially distributed population dynamics model with excitable predator-prey kinetics, where species propagate in space due to their taxis with respect to each other's gradient in addition to, or instead of, their diffusive spread. Earlier, we have described new phenomena in this model in one spatial dimension, not found in analogous systems without taxis: reflecting and self-splitting waves. Here we identify new phenomena in two spatial dimensions: unusual patterns of meander of spirals, partial reflection of waves, swelling wave tips, attachment of free wave ends to wave backs, and as a result, a novel mechanism of self-supporting complicated spatiotemporal activity, unknown in reaction-diffusion population models.

MSC 2000:: *35K57 Reaction-diffusion equations
35K50 Systems of parabolic equations, boundary value problems
37N25 Dynamical systems in biology
92D25 Population dynamics

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Zentralblatt MATH Berlin [Germany]