Motivated 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
| Identifer | oai:union.ndltd.org:arizona.edu/oai:arizona.openrepository.com:10150/622524 |
| Date | 09 May 2016 |
| Creators | Meissen, Emily P., Salau, Kehinde R., Cushing, Jim M. |
| Contributors | Department of Mathematics, University of Arizona, Interdisciplinary program in Applied Mathematics, University of Arizona |
| Publisher | TAYLOR & FRANCIS LTD |
| Source Sets | University of Arizona |
| Language | English |
| Detected Language | English |
| Type | Article |
| Rights | © 2016 Informa UK Limited, trading as Taylor & Francis Group |
| Relation | https://www.tandfonline.com/doi/full/10.1080/10236198.2016.1177522 |
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