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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.

Enrichment Paradox Induced by Spatial Heterogeneity in a Phytoplankton - Zooplankton System

J.-C. Poggiale;  M. Gauduchon;  P. Auger — 2008

Mathematical Modelling of Natural Phenomena

This paper is devoted to the study of a predator-prey model in a patchy environment. The model represents the interactions between phytoplankton and zooplankton in the water column. Two patches are considered with respect to light availability: one patch is associated to the surface layer, the second patch describes the bottom layer. We show that this spatial heterogeneity may destabilize the predator-prey system, even in oligotrophic system where the nutrient is low enough to avoid ”paradox-enrichment”...

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