Geometric method for global stability of discrete population models

Hou, Zhanyuan (2019) Geometric method for global stability of discrete population models. Discrete and Continuous Dynamical Systems (B). ISSN 1531-3492 (In Press)

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Official URL: https://www.aimsciences.org/journal/1531-3492

Abstract / Description

A class of autonomous discrete dynamical systems as population models for competing species are considered when each nullcline surface is a hyperplane. Criteria are established for global attraction of an interior or a boundary fixed point by a geometric method utilising the relative position of these nullcline planes only, independent of the growth rate function. These criteria are universal for a broad class of systems, so they can be applied directly to some known models appearing in the literature including Ricker competition models, Leslie-Gower models, Atkinson-Allen models, and generalised Atkinson-Allen models. Then global asymptotic stability is obtained by finding the eigenvalues of the Jacobian matrix at the fixed point. An intriguing question is proposed: Can a globally attracting fixed point induce a homoclinic cycle?

Item Type: Article
Uncontrolled Keywords: discrete dynamical systems, fixed points, global attraction, global asymptoticstability, geometric method, homoclinic cycle
Subjects: 500 Natural Sciences and Mathematics > 510 Mathematics
500 Natural Sciences and Mathematics > 570 Life sciences; biology
Department: School of Computing and Digital Media
Depositing User: Zhanyuan Hou
Date Deposited: 13 Nov 2019 09:14
Last Modified: 13 Nov 2019 09:14
URI: http://repository.londonmet.ac.uk/id/eprint/5298

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