Ching, A;
Baigent, S;
(2019)
The balance simplex in non-competitive 2-species scaled Lotka–Volterra systems.
Journal of Biological Dynamics
, 13
(1)
10.1080/17513758.2019.1574033.
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Abstract
Explicit expressions in terms of Gaussian Hypergeometric functions are found for a ‘balance’ manifold that connects the non-zero steady states of a 2-species, non-competitive, scaled Lotka–Volterra system by the unique heteroclinic orbits. In this model, the parameters are the interspecific interaction coefficients which affects the form of the solution used. Similar to the carrying simplex of the competitive model, this balance simplex is the common boundary of the basin of repulsion of the origin and infinity, and is smooth except possibly at steady states.
| Type: | Article |
|---|---|
| Title: | The balance simplex in non-competitive 2-species scaled Lotka–Volterra systems |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1080/17513758.2019.1574033 |
| Publisher version: | https://doi.org/10.1080/17513758.2019.1574033 |
| Language: | English |
| Additional information: | © 2019 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 License (http://creativecommons.org/ licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. |
| Keywords: | Balance simplex, Lotka–Volterra, carrying simplex, Gaussian hypergeometric function, 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/10067330 |
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