Mierczyński, J;
Baigent, S;
(2023)
Existence of the carrying simplex for a retrotone map.
Journal of Difference Equations and Applications
10.1080/10236198.2023.2285394.
(In press).
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Abstract
We present a dynamical approach to the study of unordered, attracting manifolds of retrotone maps commonly known as carrying simplices. Our approach is novel in that it uses the radial representation of unordered manifolds over the probability simplex coupled with distances between these manifolds measured by way of the Harnack and Hausdorff metrics. We establish Kuratowski convergence of radial representations of unordered manifolds to a unique function which then provides the locally Lipschitz radial representation of the carrying simplex.
| Type: | Article |
|---|---|
| Title: | Existence of the carrying simplex for a retrotone map |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1080/10236198.2023.2285394 |
| Publisher version: | https://doi.org/10.1080/10236198.2023.2285394 |
| Language: | English |
| Additional information: | This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third-party material in this article are included in the Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/ |
| Keywords: | Competitive maps, retro, tone maps, carrying simplices, attractors |
| 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/10183280 |
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