eprintid: 10049790 rev_number: 22 eprint_status: archive userid: 608 dir: disk0/10/04/97/90 datestamp: 2018-06-11 11:48:56 lastmod: 2020-02-12 18:14:44 status_changed: 2018-06-11 11:48:56 type: article metadata_visibility: show creators_name: Baigent, S title: Convex geometry of the carrying simplex for the May-Leonard map ispublished: pub divisions: UCL divisions: A01 divisions: B04 divisions: C06 divisions: F59 keywords: Carrying simplex, convexity, concavity, May-Leonard map, invariant manifold note: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. abstract: 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. date: 2019-04 date_type: published publisher: American Institute of Mathematical Sciences official_url: http://dx.doi.org/10.3934/dcdsb.2018288 oa_status: green full_text_type: other language: eng primo: open primo_central: open_green verified: verified_manual elements_id: 1560183 doi: 10.3934/dcdsb.2018288 lyricists_name: Baigent, Stephen lyricists_id: SABAI49 actors_name: Baigent, Stephen actors_id: SABAI49 actors_role: owner full_text_status: public publication: Discrete and Continuous Dynamical Systems - Series B volume: 24 number: 4 pagerange: 1697-1723 issn: 1531-3492 citation: Baigent, S; (2019) Convex geometry of the carrying simplex for the May-Leonard map. Discrete and Continuous Dynamical Systems - Series B , 24 (4) pp. 1697-1723. 10.3934/dcdsb.2018288 <https://doi.org/10.3934/dcdsb.2018288>. Green open access document_url: https://discovery.ucl.ac.uk/id/eprint/10049790/1/map2convexDCDSFinal.pdf