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Convexity-preserving flows of totally competitive planar Lotka-Volterra equations and the geometry of the carrying simplex

Baigent, SA; (2012) Convexity-preserving flows of totally competitive planar Lotka-Volterra equations and the geometry of the carrying simplex. Proceedings of the Edinburgh Mathematical Society , 55 (1) 53 - 63. 10.1017/S0013091510000684.

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Abstract

We show that the flow generated by the totally competitive planar Lotka-Volterra equations deforms the line connecting the two axial equilibria into convex or concave curves, and that these curves remain convex or concave for all subsequent time. We apply the observation to provide an alternative proof to that given by Tineo that the carrying simplex, the globally attracting invariant manifold that joins the axial equilibria, is either convex, concave or a straight line segment.

Type: Article
Title: Convexity-preserving flows of totally competitive planar Lotka-Volterra equations and the geometry of the carrying simplex
Location: UK
DOI: 10.1017/S0013091510000684
Publisher version: http://journals.cambridge.org/action/displayAbstra...
Keywords: Lotka-Volterra equations, Curvature-preserving flow, Competitive dynamics, Carrying Simplex
UCL classification: UCL > School of BEAMS > Faculty of Maths and Physical Sciences > Mathematics
URI: http://discovery.ucl.ac.uk/id/eprint/741122
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