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dc.contributor.authorCushing, J. M.
dc.contributor.authorFarrell, Alex P.
dc.date.accessioned2020-01-16T19:31:17Z
dc.date.available2020-01-16T19:31:17Z
dc.date.issued2019-12-08
dc.identifier.citationJ. M. Cushing & Alex P. Farrell (2019) A bifurcation theorem for nonlinear matrix models of population dynamics, Journal of Difference Equations and Applications, DOI: 10.1080/10236198.2019.1699916en_US
dc.identifier.issn1023-6198
dc.identifier.doi10.1080/10236198.2019.1699916
dc.identifier.urihttp://hdl.handle.net/10150/636479
dc.description.abstractWe prove a general theorem for nonlinear matrix models of the type used in structured population dynamics that describes the bifurcation that occurs when the extinction equilibrium destabilizes as a model parameter is varied. The existence of a bifurcating continuum of positive equilibria is established, and their local stability is related to the direction of bifurcation. Our theorem generalizes existing theorems found in the literature in two ways. First, it allows for a general appearance of the bifurcation parameter (existing theorems require the parameter to appear linearly). This significantly widens the applicability of the theorem to population models. Second, our theorem describes circumstances in which a backward bifurcation can produce stable positive equilibria (existing theorems allow for stability only when the bifurcation is forward). The signs of two diagnostic quantities determine the stability of the bifurcating equilibrium and the direction of bifurcation. We give examples that illustrate these features.en_US
dc.description.sponsorshipNSFNational Science Foundation (NSF) [DMS-1407564]en_US
dc.language.isoenen_US
dc.publisherTAYLOR & FRANCIS LTDen_US
dc.rights© 2019 Informa UK Limited, trading as Taylor & Francis Groupen_US
dc.subjectNonlinear difference equationsen_US
dc.subjectmatrix equationsen_US
dc.subjectpopulation dynamicsen_US
dc.subjectequilibriumen_US
dc.subjectbifurcationen_US
dc.subjectstabilityen_US
dc.titleA bifurcation theorem for nonlinear matrix models of population dynamicsen_US
dc.typeArticleen_US
dc.contributor.departmentUniv Arizona, Dept Mathen_US
dc.identifier.journalJOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONSen_US
dc.description.note12 month embargo; published online: 8 December 2019en_US
dc.description.collectioninformationThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu.en_US
dc.eprint.versionFinal accepted manuscripten_US
dc.source.beginpage1-20


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