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Pursuit-evasion predator-prey waves in two spatial dimensions. (English) Zbl 1080.35036
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:
35K57Reaction-diffusion equations
35K50Systems of parabolic equations, boundary value problems (MSC2000)
37N25Dynamical systems in biology
92D25Population dynamics (general)