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Zbl 0978.92033
Wang, Mei-Hui; Kot, Mark
Speeds of invasion in a model with strong or weak Allee effects. (English)
[J] Math. Biosci. 171, No.1, 83-97 (2001). ISSN 0025-5564

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 2000:: *92D40 Ecology
35Q80 Appl. of PDE in areas other than physics
35K57 Reaction-diffusion equations

Keywords: travelling waves; strong Allee effects; invasion model; weak Allee effects; linearization

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