BIFURCATION-ANALYSIS OF A METAPOPULATION MODEL WITH SOURCES AND SINKS

A class of functions describing the Allee effect and local catastrophe s in population dynamics is introduced and the behaviour of the result ing one-dimensional discrete dynamical system is investigated in detai l. The main topic of the paper is a treatment of the two-dimensional s ystem arising when an Allee function is coupled with a function descri bing the population decay in a so-called sink. New types of bifurcatio n phenomena are discovered and explained. The relevance of the results for metapopulation dynamics is discussed.