Analytic considerations in the study of spatial patterns arising from non-local interaction effects in population dynamics.

M. FUENTES; M. N. KUPERMAN; V. M. KENKRE

JOURNAL OF PHYSICAL CHEMISTRY B

Año: 2004 vol. 108 p. 10505 - 10508

1089-5647

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.