Geometric method for global stability and repulsion in Kolmogorov systems
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 fo...
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| Format: | Article |
| Language: | English |
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Taylor & Francis
2018
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| Online Access: | https://repository.londonmet.ac.uk/4039/1/Geometric%20method%20for%20glovbal%20tability%20and%20repulsion.pdf |
| _version_ | 1825625242981105664 |
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| author | Hou, Zhanyuan |
| author_facet | Hou, Zhanyuan |
| author_sort | Hou, Zhanyuan |
| collection | LMU |
| 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. |
| first_indexed | 2024-07-09T03:55:53Z |
| format | Article |
| id | oai:repository.londonmet.ac.uk:4039 |
| institution | London Metropolitan University |
| language | English |
| last_indexed | 2024-07-09T03:55:53Z |
| publishDate | 2018 |
| publisher | Taylor & Francis |
| record_format | eprints |
| spelling | oai:repository.londonmet.ac.uk:40392019-08-09T10:48:11Z https://repository.londonmet.ac.uk/4039/ Geometric method for global stability and repulsion in Kolmogorov systems Hou, Zhanyuan 510 Mathematics 570 Life sciences; biology 580 Plants (Botany) 590 Animals (Zoology) 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. Taylor & Francis 2018-12-14 Article PeerReviewed text en https://repository.londonmet.ac.uk/4039/1/Geometric%20method%20for%20glovbal%20tability%20and%20repulsion.pdf Hou, Zhanyuan (2018) Geometric method for global stability and repulsion in Kolmogorov systems. Dynamical systems, 34 (3). pp. 456-483. ISSN 1468-9367 10.1080/14689367.2018.1554030 10.1080/14689367.2018.1554030 |
| spellingShingle | 510 Mathematics 570 Life sciences; biology 580 Plants (Botany) 590 Animals (Zoology) Hou, Zhanyuan Geometric method for global stability and repulsion in Kolmogorov systems |
| title | Geometric method for global stability and repulsion in Kolmogorov systems |
| title_full | Geometric method for global stability and repulsion in Kolmogorov systems |
| title_fullStr | Geometric method for global stability and repulsion in Kolmogorov systems |
| title_full_unstemmed | Geometric method for global stability and repulsion in Kolmogorov systems |
| title_short | Geometric method for global stability and repulsion in Kolmogorov systems |
| title_sort | geometric method for global stability and repulsion in kolmogorov systems |
| topic | 510 Mathematics 570 Life sciences; biology 580 Plants (Botany) 590 Animals (Zoology) |
| url | https://repository.londonmet.ac.uk/4039/1/Geometric%20method%20for%20glovbal%20tability%20and%20repulsion.pdf |
| work_keys_str_mv | AT houzhanyuan geometricmethodforglobalstabilityandrepulsioninkolmogorovsystems |