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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.
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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