Abstract

Simple analytical considerations are applied to recently discovered patterns in a generalized Fisher equation. The generalization consists of the inclusion of nonlocal competition interactions among the constituents of the field exhibiting patterns. We show here how stability arguments yield a necessary condition for pattern formation involving the ratio of the pattern wavelength and the effective diffusion length of the individual constituents. We also remark on how a mode-mode coupling analysis may be developed that might be useful in shedding some light on the amplitude of the patterns.