The global stability of coexisting equilibria for three models of mutualism
We analyze the dynamics of three models of mutualism, establishing the global stability of coexisting equilibria by means of Lyapunov's second method. This further establishes the usefulness of certain Lyapunov functionals of an abstract nature introduced in an earlier paper. As a consequence,...
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| Format: | Article |
| Language: | English |
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AIMS Press
2015-09-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2016.13.101 |
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| author | Paul Georgescu Hong Zhang Daniel Maxin |
| author_facet | Paul Georgescu Hong Zhang Daniel Maxin |
| author_sort | Paul Georgescu |
| collection | DOAJ |
| description | We analyze the dynamics of three models of mutualism, establishing the global stability of coexisting equilibria by means of Lyapunov's second method. This further establishes the usefulness of certain Lyapunov functionals of an abstract nature introduced in an earlier paper. As a consequence, it is seen that the use of higher order self-limiting terms cures the shortcomings of Lotka-Volterra mutualisms, preventing unbounded growth and promoting global stability. |
| format | Article |
| id | doaj-art-68001de85ad2455dae8a6c91a16a44df |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2015-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-68001de85ad2455dae8a6c91a16a44df2025-01-24T02:34:05ZengAIMS PressMathematical Biosciences and Engineering1551-00182015-09-0113110111810.3934/mbe.2016.13.101The global stability of coexisting equilibria for three models of mutualismPaul Georgescu0Hong Zhang1Daniel Maxin2Department of Mathematics, Technical University of Iaşi, Bd. Copou 11, 700506 IaşiDepartment of Financial Mathematics, Jiangsu University, ZhenJiang, Jiangsu, 212013Department of Financial Mathematics, Jiangsu University, ZhenJiang, Jiangsu, 212013We analyze the dynamics of three models of mutualism, establishing the global stability of coexisting equilibria by means of Lyapunov's second method. This further establishes the usefulness of certain Lyapunov functionals of an abstract nature introduced in an earlier paper. As a consequence, it is seen that the use of higher order self-limiting terms cures the shortcomings of Lotka-Volterra mutualisms, preventing unbounded growth and promoting global stability.https://www.aimspress.com/article/doi/10.3934/mbe.2016.13.101monotonicity properties.global stabilitymutualistic interactionlyapunov functionalinvariance principle |
| spellingShingle | Paul Georgescu Hong Zhang Daniel Maxin The global stability of coexisting equilibria for three models of mutualism Mathematical Biosciences and Engineering monotonicity properties. global stability mutualistic interaction lyapunov functional invariance principle |
| title | The global stability of coexisting equilibria for three models of mutualism |
| title_full | The global stability of coexisting equilibria for three models of mutualism |
| title_fullStr | The global stability of coexisting equilibria for three models of mutualism |
| title_full_unstemmed | The global stability of coexisting equilibria for three models of mutualism |
| title_short | The global stability of coexisting equilibria for three models of mutualism |
| title_sort | global stability of coexisting equilibria for three models of mutualism |
| topic | monotonicity properties. global stability mutualistic interaction lyapunov functional invariance principle |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2016.13.101 |
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