Global stability of discrete-time competitive population models

Baigent, Stephen and Hou, Zhanyuan (2017) Global stability of discrete-time competitive population models. Journal of Difference Equations with Applications, 23 (2017). ISSN 1023-6198 (print) 1563-5120 (online)

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Abstract

We develop practical tests for the global asymptotic stability of interior fixed points for discrete-time competitive population models. Our method constitutes the extension to maps of the Split Lyapunov method developed for differential equations. We give ecologically-motivated sufficient conditions for global stability of an interior fixed point of a map of Kolmogorov form. We introduce the concept of a principal reproductive mode, which is linked to a normal at the interior fixed point of a hypersurface of vanishing weighted-average growth. Our method is applied to establish new global stability results for 3-species competitive systems of May-Leonard type, where previously only parameter values for local stability was known.

Item Type: Article
Uncontrolled Keywords: competitive Kolmogorov maps; global stability; Leslie-Gower; Ricker; principal reproductive mode
Subjects: 500 Natural Sciences and Mathemetics > 510 Mathematics
500 Natural Sciences and Mathemetics > 570 Life sciences; biology
Department: School of Computing and Digital Media
Depositing User: Zhanyuan Hou
Date Deposited: 20 Jun 2017 08:17
Last Modified: 12 Jul 2017 08:43
URI: http://repository.londonmet.ac.uk/id/eprint/1227

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