Yeganeh, HN;
Baigent, S;
(2024)
Convexity of non-compact carrying simplices in logarithmic coordinates.
Journal of Difference Equations and Applications
, 30
(10)
pp. 1671-1691.
10.1080/10236198.2024.2369215.
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Abstract
We study a non-compact version of the carrying simplex for the planar Leslie–Gower and planar Ricker maps when they are written in logarithmic variables. We show that for both of these models there is a convex (unbounded) invariant set (Formula presented.), and all orbits are attracted to (Formula presented.). For the Leslie–Gower map, which is injective, the boundary of (Formula presented.) globally attracts all orbits and we identify it with a non-compact carrying simplex. As the Ricker map is not invertible, the boundary of (Formula presented.) may not be invariant. We establish conditions on the parameters of the Ricker map which guarantee that there is a convex non-compact carrying simplex when r, s<1 which maps into a compact carrying simplex in the standard untransformed coordinates.
| Type: | Article |
|---|---|
| Title: | Convexity of non-compact carrying simplices in logarithmic coordinates |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1080/10236198.2024.2369215 |
| Publisher version: | http://dx.doi.org/10.1080/10236198.2024.2369215 |
| Language: | English |
| Additional information: | © 2024 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group. This is an Open Access article distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives License (http://creativecommons.org/licenses/by-nc-nd/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited, and is not altered, transformed, or built upon in any way. The terms on which this article has been published allow the posting of the Accepted Manuscript in a repository by the author(s) or with their consent. |
| Keywords: | Carrying simplex, invariant manifold, convexity, Ricker map, Leslie–Gower map |
| UCL classification: | UCL 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-pp.ucl.ac.uk/id/eprint/10197962 |
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