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competitive dynamics

Proceedings of the Edinburgh Mathematical Society (1)

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Convexity-preserving flows of totally competitive planar Lotka–Volterra equations and the geometry of the carrying simplex
Part of
Stephen Baigent
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 55 / Issue 1 / February 2012

Published online by Cambridge University Press:

01 November 2011, pp. 53-63
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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 in 2001 that the carrying simplex, the globally attracting invariant manifold that joins the axial equilibria, is either convex, concave or a straight-line segment.