Hou, Zhanyuan (2020) Geometric method for global stability of discrete population models. Discrete and Continuous Dynamical Systems (B), 25 (9). pp. 3305-3334. ISSN 1531-3492
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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 |
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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: | 15 Mar 2021 11:47 |
URI: | https://repository.londonmet.ac.uk/id/eprint/5298 |
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