A note on global stability of three-dimensional Ricker models

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Gyllenberg , M , Jiang , J & Niu , L 2019 , ' A note on global stability of three-dimensional Ricker models ' , Journal of Difference Equations and Applications , vol. 25 , no. 1 , pp. 142-150 . https://doi.org/10.1080/10236198.2019.1566459

Title: A note on global stability of three-dimensional Ricker models
Author: Gyllenberg, Mats; Jiang, Jifa; Niu, Lei
Contributor: University of Helsinki, Department of Mathematics and Statistics
University of Helsinki, Department of Mathematics and Statistics
Date: 2019-01-02
Language: eng
Number of pages: 9
Belongs to series: Journal of Difference Equations and Applications
ISSN: 1023-6198
URI: http://hdl.handle.net/10138/299977
Abstract: In the recent paper [E. C. Balreira, S. Elaydi, and R. Luis, J. Differ. Equ. Appl. 23 (2017), pp. 2037-2071], Balreira, Elaydi and Luis established a good criterion for competitive mappings to have a globally asymptotically stable interior fixed point by a geometric approach. This criterion can be applied to three dimensional Kolmogorov competitive mappings on a monotone region with a carrying simplex whose planar fixed points are saddles but globally asymptotically stable on their positive coordinate planes. For three dimensional Ricker models, they found mild conditions on parameters such that the criterion can be applied to. Observing that Balreira, Elaydi and Luis' discussion is still valid for the monotone region with piecewise smooth boundary, we prove in this note that the interior fixed point of three dimensional Kolmogorov competitive mappings is globally asymptotically stable if they admit a carrying simplex and three planar fixed points which are saddles but globally asymptotically stable on their positive coordinate planes. This result is much easier to apply in the application.
Subject: 111 Mathematics
Global stability
Ricker model
carrying simplex
global dynamics
phase portrait
37Cxx
CARRYING SIMPLEX
DYNAMICS
CLASSIFICATION
BOUNDARY
Global stability
Ricker model
carrying simplex
global dynamics
phase portrait
37Cxx
CARRYING SIMPLEX
DYNAMICS
CLASSIFICATION
BOUNDARY
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