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Nonmonotone invariant manifolds in the Nagylaki–Crow model

Seymenoglu, B; Baigent, SA; (2018) Nonmonotone invariant manifolds in the Nagylaki–Crow model. Nonlinear Analysis: Real World Applications , 41 pp. 570-587. 10.1016/j.nonrwa.2017.11.011. Green open access

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Abstract

We use a change of dynamical variables to prove, subject to certain conditions on the parameters, that a nonmonotone invariant manifold exists and is the graph of a convex function for the planar Nagylaki–Crow fertility–mortality model from population genetics with n = 2. Our results are obtained without the common assumption that fertilities or death rates are additive, and are not restricted to the case that the model is competitive in the new coordinates. We also provide numerical examples demonstrating that the manifold need not be the graph of a convex function, smooth, unique or globally attracting, and that the model exhibits a sequence of nonmonotone manifolds similar to those studied by Hirsch for competitive Kolmogorov systems (Hirsch 1988).

Type: Article
Title: Nonmonotone invariant manifolds in the Nagylaki–Crow model
Open access status: An open access version is available from UCL Discovery
DOI: 10.1016/j.nonrwa.2017.11.011
Publisher version: https://doi.org/10.1016/j.nonrwa.2017.11.011
Language: English
Additional information: © 2017 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
Keywords: Invariant manifolds, Population genetics, Nagylaki–Crow model
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/10041366
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