Analytic considerations in the study of spatial patterns arising from non-local interaction effects in population dynamics
M. A. Fuentes, M. N. Kuperman, V. M. Kenkre
Abstract
Simple analytic considerations are applied to recently discovered patterns in a generalized Fisher equation for population dynamics. The generalization consists of the inclusion of non-local competition interactions among individuals. We first show how stability arguments yield a condition for pattern formation involving the ratio of the pattern wavelength and the effective diffusion length of the individuals. We develop a mode-mode coupling analysis which might be useful in shedding some light on the observed formation of small-amplitude versus large-amplitude patterns.
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