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Extinction conditions for isolated populations with Allee effect. (English) Zbl 1217.92080
Summary: One of the main ecological phenomenons is the Allee effect [see W. C. Allee, The social life of animals. London: W. Heinemann (1938)], in which a positive benefit from the presence of conspecifics arises. We describe the dynamical behavior of a population with Allee effect in a finite domain that is surrounded by a completely hostile environment. Using spectral methods to rewrite the local density of habitants we are able to determine the critical patch size and the bifurcation diagram, hence characterizing the stability of possible solutions, for different ways to introduce the Allee effect in the reaction-diffusion equations.

MSC:
92D40 Ecology
92D50 Animal behavior
37N25 Dynamical systems in biology
35Q92 PDEs in connection with biology, chemistry and other natural sciences
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