Baigent, S;
(2019)
Convex geometry of the carrying simplex for the May-Leonard map.
Discrete and Continuous Dynamical Systems - Series B
, 24
(4)
pp. 1697-1723.
10.3934/dcdsb.2018288.
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Abstract
We study the convex geometry of certain invariant manifolds, known as carrying simplices, for 3-species competitive Kolmogorov-type maps. We show that if all planes whose normal bundles are contained in a fixed closed and solid convex cone are rendered convex (concave) surfaces by the map, then, if there is a carrying simplex, it is a convex (concave) surface. We apply our results to the May-Leonard map.
| Type: | Article |
|---|---|
| Title: | Convex geometry of the carrying simplex for the May-Leonard map |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.3934/dcdsb.2018288 |
| Publisher version: | http://dx.doi.org/10.3934/dcdsb.2018288 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Carrying simplex, convexity, concavity, May-Leonard map, invariant manifold |
| 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/10049790 |
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