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Pattern and Waves for a Model in Population Dynamics with Nonlocal Consumption of Resources

S. Genieys, V. Volpert, P. Auger (2010)

Mathematical Modelling of Natural Phenomena

We study a reaction-diffusion equation with an integral term describing nonlocal consumption of resources in population dynamics. We show that a homogeneous equilibrium can lose its stability resulting in appearance of stationary spatial structures. They can be related to the emergence of biological species due to the intra-specific competition and random mutations. Various types of travelling waves are observed.

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