1990/12/01 by N. F. Britton · 2 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Medicine · #Evolution and Genetic Dynamics #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear Dynamics and Pattern Formation
paper · doi:10.1137/0150099
crossref issued 1990/12/01 · crossref published 1990/12/01 · crossref published-print 1990/12/01 · openalex publication_date 1990/12/01 · crossref created 2005/02/23 · crossref deposited 2017/01/29 · openalex created_date 2025/10/10 · crossref indexed 2026/07/30 · openalex updated_date 2026/07/30
An integro-differential reaction-diffusion equation is proposed as a model for populations where local aggregation is advantageous but intraspecific competition increases as global populations increase. It is claimed that this is inherently more realistic than the usual kind of reaction-diffusion model for mobile populations. Three kinds of bifurcation from the uniform steady-state solution are considered, (i) to steady spatially periodic structures, (ii) to periodic standing wave solutions, and (iii) to periodic travelling wave solutions. These correspond to aggregation and motion of populations.