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.
@article{arxiv.math/0511687,
title = {On a New Mechanism of Pattern Formation in Population Dynamics},
author = {Stephane Genieys and Vitaly Volpert and Pierre Auger},
journal= {arXiv preprint arXiv:math/0511687},
year = {2007}
}