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On a New Mechanism of Pattern Formation in Population Dynamics

Research paper by Stephane Genieys, Vitaly Volpert, Pierre Auger

Indexed on: 28 Nov '05Published on: 28 Nov '05Published in: Mathematics - Analysis of PDEs



Abstract

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.