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Balance simplices of 3-species May-Leonard systems

Baigent, S; Ching, A; (2020) Balance simplices of 3-species May-Leonard systems. Journal of Biological Dynamics , 14 (1) pp. 187-199. 10.1080/17513758.2020.1736656. Green open access

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Abstract

We investigate the existence of a two-dimensional invariant manifold that attracts all nonzero orbits in 3 species Lotka-Volterra systems with identical linear growth rates. This manifold, which we call the balance simplex, is the common boundary of the basin of repulsion of the origin and the basin of repulsion of infinity. The balance simplex is linked to ecological models where there is 'growth when rare' and competition for finite resources. By including alternative food sources for predators we cater for predator-prey type models. In the case that the model is competitive, the balance simplex coincides with the carrying simplex which is an unordered manifold (no two points may be ordered componentwise), but for non-competitive models the balance simplex need not be unordered. The balance simplex of our models contains all limit sets and is the graph of a piecewise analytic function over the unit probability simplex.

Type: Article
Title: Balance simplices of 3-species May-Leonard systems
Location: England
Open access status: An open access version is available from UCL Discovery
DOI: 10.1080/17513758.2020.1736656
Publisher version: https://doi.org/10.1080/17513758.2020.1736656
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: 24C45, 37D10, 92D40, Balance simplex, Lotka-Volterra, invariant manifold, stability basin boundaries
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/10093501
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