Geometric method for global stability and repulsion in Kolmogorov systems

Hou, Zhanyuan (2018) Geometric method for global stability and repulsion in Kolmogorov systems. Dynamical systems, 34 (3). pp. 456-483. ISSN 1468-9367

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Abstract / Description

A class of autonomous Kolmogorov systems that are dissipative and competitive with the origin as a repellor are considered when each nullcline surface is either concave or convex. Geometric method is developed by using the relative positions of the upper and lower planes of the nullcline surfaces for global asymptotic stability of an interior or a boundary equilibrium point. Criteria are also established for global repulsion of an interior or a boundary equilibrium point on the carrying simplex. This method and the theorems can be viewed as a natural extension of those results for Lotka-Volterra systems in the literature.

Item Type:	Article
Uncontrolled Keywords:	equilibrium point, global attraction, global repulsion, global asymptotic stability, geometric method, Kolmogorov systems
Subjects:	500 Natural Sciences and Mathematics > 510 Mathematics 500 Natural Sciences and Mathematics > 570 Life sciences; biology 500 Natural Sciences and Mathematics > 580 Plants (Botany) 500 Natural Sciences and Mathematics > 590 Animals (Zoology)
Department:	School of Computing and Digital Media
Depositing User:	Zhanyuan Hou
Date Deposited:	04 Dec 2018 16:37
Last Modified:	09 Aug 2019 10:48
URI:	https://repository.londonmet.ac.uk/id/eprint/4039

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