Summary
A class of functions describing the Allee effect and local catastrophes in population dynamics is introduced and the behaviour of the resulting one-dimensional discrete dynamical system is investigated in detail. The main topic of the paper is a treatment of the two-dimensional system arising when an Allee function is coupled with a function describing the population decay in a so-called sink. New types of bifurcation phenomena are discovered and explained. The relevance of the results for metapopulation dynamics is discussed.
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Communicated by Stephen Wiggins
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Gyllenberg, M., Osipov, A.V. & Söderbacka, G. Bifurcation analysis of a metapopulation model with sources and sinks. J Nonlinear Sci 6, 329–366 (1996). https://doi.org/10.1007/BF02433474
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DOI: https://doi.org/10.1007/BF02433474