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Speeds of invasion in a model with strong or weak Allee effects. (English) Zbl 0978.92033
Summary: We study an invasion model based on a reaction-diffusion equation with an Allee effect. We use a special, piecewise-linear, population growth rate. This function allows us to obtain traveling wave solutions and to compute wave speeds for a full range of Allee effects, including weak Allee effects. Some investigators claim that linearization fails to give the correct speed of invasion if there is an Allee effect. We show that the minimum speed for a sufficiently weak Allee may, in fact, be the same as that derived by means of linearization.

MSC:
92D40 Ecology
35Q92 PDEs in connection with biology, chemistry and other natural sciences
35K57 Reaction-diffusion equations
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