2005/11/28 by Stephane Genieys, Stéphane Génieys, Genieys, Stephane +4
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · Social Sciences · #35P15 #45K05 #92D15 #Analysis of PDEs (math.AP) #Demography #Dynamics (music) #Evolution and Genetic Dynamics #Evolutionary Game Theory and Cooperation #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Mechanism (biology) #Physics #Population #Sociology #math.AP #msc:35P15 #msc:45K05 #msc:92D15
paper · pdf · open access · doi:10.48550/arxiv.math/0511687
arxiv created 2005/11/28 · openalex publication_date 2005/11/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study a reaction-diffusion equation with an integral term describing nonlocal consumption of resources. We show that a homogeneous equilibrium can lose its stability resulting in appearance of stationary spatial structures. It is a new mechanism of pattern formation in population dynamics that can explain emergence of biological species due to intra-specific competition and random mutations.Travelling waves connecting an unstable homogeneous equilibrium and a periodic in space stationary solution are studied numerically.