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.
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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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