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Published on: July 4, 2007
Dynamics in an almost periodic metapopulation with competition and habitat destruction: An exponential dichotomy
Pablo Amster1, Gonzalo Robledo2, Daniel Sepúlveda3
1Argentina.
Abstract:
This paper explains how the theory of exponential dichotomy allows to carry out the study of an almost periodic version of a metapopulation model developed in the 90's, which generalizes the classical Levins approach by considering species in competition affected by habitat destruction. The metapopulation dynamics is determined by the balance between the forces of extinction and colonization, where the last ones are affected by habitat destruction. We show that the average predominance of one of these forces is equivalent to the property of exponential dichotomy of a scalar linear differential equation allowing to carry out a recursive and exhaustive description of persistence/extinction scenarios. In addition, we start a preliminary discussion describing a more elusive behavior when the colonization and extinction forces are similar in average and the dichotomy is no more verified.
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