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Main Authors: Niu, Lei, Xie, Xizhuang
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2402.19213
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author Niu, Lei
Xie, Xizhuang
author_facet Niu, Lei
Xie, Xizhuang
contents In this paper, we are concerned with the permanence of a Lotka-Volterra model of three competing species with seasonal succession. Based on the existence of a carrying simplex, that is a globally attracting hypersurface of codimension one, we provide a complete classification of the permanence and impermanence in terms of inequalities on the parameters of this model. Moreover, we numerically show that invariant closed curves can occur in the permanent classes, which means that the positive fixed point of the associated Poincare map in the permanent classes is not always globally asymptotically stable.
format Preprint
id arxiv_https___arxiv_org_abs_2402_19213
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Classification of permanence and impermanence for a Lotka-Volterra model of three competing species with seasonal succession
Niu, Lei
Xie, Xizhuang
Dynamical Systems
37N25, 92D25
In this paper, we are concerned with the permanence of a Lotka-Volterra model of three competing species with seasonal succession. Based on the existence of a carrying simplex, that is a globally attracting hypersurface of codimension one, we provide a complete classification of the permanence and impermanence in terms of inequalities on the parameters of this model. Moreover, we numerically show that invariant closed curves can occur in the permanent classes, which means that the positive fixed point of the associated Poincare map in the permanent classes is not always globally asymptotically stable.
title Classification of permanence and impermanence for a Lotka-Volterra model of three competing species with seasonal succession
topic Dynamical Systems
37N25, 92D25
url https://arxiv.org/abs/2402.19213