On a New Mechanism of Pattern Formation in Population Dynamics

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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.

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Analysis of PDEs, 92D15, 45K05, 35P15

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http://salesiana.dossiersoluciones.com/handle/123456789/105116

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0511687
 http://arxiv.org/abs/math/0511687

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arXiv