Pursuit-evasion predator-prey waves in two spatial dimensions

Details Pursuit-evasion predator-prey waves in two spatial dimensions Pursuit-evasion predator-prey waves in two spatial dimensions

2004-06-08

arxiv.org/abs/nlin/0406012v1

Nonlinear Sciences

Pattern Formation and Solitons

15 pages, 15 figures, submitted to Chaos

Scientific paper

10.1063/1.1793751

We consider a spatially distributed population dynamics model with excitable predator-prey dynamics, 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 wavetips, attachment of free wave ends to wave backs, and as a result, a novel mechanism of self-supporting complicated spatio-temporal activity, unknown in reaction-diffusion population models.

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