Linearization and invariant manifolds on the carrying simplex for competitive maps

Show full item record



Permalink

http://hdl.handle.net/10138/307025

Citation

Mierczynski , J , Niu , L & Ruiz-Herrera , A 2019 , ' Linearization and invariant manifolds on the carrying simplex for competitive maps ' , Journal of Differential Equations , vol. 267 , no. 12 , pp. 7385-7410 . https://doi.org/10.1016/j.jde.2019.08.001

Title: Linearization and invariant manifolds on the carrying simplex for competitive maps
Author: Mierczynski, Janusz; Niu, Lei; Ruiz-Herrera, Alfonso
Contributor: University of Helsinki, Department of Mathematics and Statistics
Date: 2019-12-05
Language: eng
Number of pages: 26
Belongs to series: Journal of Differential Equations
ISSN: 0022-0396
URI: http://hdl.handle.net/10138/307025
Abstract: A result due to M.W. Hirsch states that most competitive maps admit a carrying simplex, i.e., an invariant hypersurface of codimension one which attracts all nontrivial orbits. The common approach in the study of these maps is to focus on the dynamical behavior on the carrying simplex. However, this manifold is normally non-smooth. Therefore, not every tool coming from Differential Geometry can be applied. In this paper we prove that the restriction of the map to the carrying simplex in a neighborhood of an interior fixed point is topologically conjugate to the restriction of the map to its pseudo-unstable manifold by an invariant foliation. This implies that the linearization techniques are applicable for studying the local dynamics of the interior fixed points on the carrying simplex. We further construct the stable and unstable manifolds on the carrying simplex. Our results give partial responses to Hirsch's problem regarding the smoothness of the carrying simplex. We discuss some applications in classical models of population dynamics. (C) 2019 Elsevier Inc. All rights reserved.
Subject: Carrying simplex
Invariant foliation
Pseudo-stable manifold
Pseudo-unstable manifold
Linearization
Invariant manifold
EQUIVALENT CLASSIFICATION
DIFFERENTIAL-EQUATIONS
GLOBAL STABILITY
DISCRETE
SYSTEMS
SIMPLICES
DYNAMICS
MODELS
SMOOTHNESS
FOLIATIONS
111 Mathematics
Rights:


Files in this item

Total number of downloads: Loading...

Files Size Format View
Linearization_accepted_manuscript.pdf 431.3Kb PDF View/Open

This item appears in the following Collection(s)

Show full item record