AffiliationDepartment of Mathematics, University of Arizona
Interdisciplinary program in Applied Mathematics, University of Arizona
MetadataShow full item record
PublisherTAYLOR & FRANCIS LTD
CitationA global bifurcation theorem for Darwinian matrix models 2016, 22 (8):1114 Journal of Difference Equations and Applications
Rights© 2016 Informa UK Limited, trading as Taylor & Francis Group
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AbstractMotivated by models from evolutionary population dynamics, we study a general class of nonlinear difference equations called matrix models. Under the assumption that the projection matrix is non-negative and irreducible, we prove a theorem that establishes the global existence of a continuum with positive equilibria that bifurcates from an extinction equilibrium at a value of a model parameter at which the extinction equilibrium destabilizes. We give criteria for the global shape of the continuum, including local direction of bifurcation and its relationship to the local stability of the bifurcating positive equilibria. We discuss a relationship between backward bifurcations and Allee effects. Illustrative examples are given
NotePublished online: 09 May 2016; 6 month embargo.
VersionFinal accepted manuscript