On a New Mechanism of Pattern Formation in Population Dynamics

2005/11/28 by Genieys, Stephane, Volpert, Vitaly, Auger, Pierre
#35P15 #45K05 #92D15 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0511687

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.

Related

• Doubly nonlocal reaction-diffusion equation and the emergence of species
• Analytic considerations in the study of spatial patterns arising from non-local interaction effects in population dynamics
• Effect of spatial average on the spatiotemporal pattern formation of reaction-diffusion systems
• Pattern formation in dense populations studied by inference of nonlinear diffusion-reaction mechanisms
• Spatiotemporal pattern formation of Beddington-DeAngelis-type predator-prey model