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