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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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.
|Title:||Convexity-preserving flows of totally competitive planar Lotka-Volterra equations and the geometry of the carrying simplex|
|Keywords:||Lotka-Volterra equations, Curvature-preserving flow, Competitive dynamics, Carrying Simplex|
|UCL classification:||UCL > School of BEAMS > Faculty of Maths and Physical Sciences > Mathematics|
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