%0 Journal Article
%@ 1531-3492
%A Baigent, S
%D 2019
%F discovery:10049790
%I American Institute of Mathematical Sciences
%J Discrete and Continuous Dynamical Systems - Series B
%K Carrying simplex, convexity, concavity, May-Leonard map, invariant manifold
%N 4
%P 1697-1723
%T Convex geometry of the carrying simplex for the May-Leonard map
%U https://discovery.ucl.ac.uk/id/eprint/10049790/
%V 24
%X We study the convex geometry of certain invariant manifolds, known as carrying simplices, for 3-species competitive Kolmogorov-type maps. We show that if all planes whose normal bundles are contained in a fixed closed and solid convex cone are rendered convex (concave) surfaces by the map, then, if there is a carrying simplex, it is a convex (concave) surface. We apply our results to the May-Leonard map.
%Z This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.