Dynamics of competitive systems with a single common limiting factor
The concept of limiting factors (or regulating factors) succeeded in formulating the well-known principle of competitive exclusion.This paper shows that the concept of limiting factors is helpful not only to formulate the competitive exclusion principle, but also to obtain other ecological insights....
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| Format: | Article |
| Language: | English |
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AIMS Press
2014-11-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.71 |
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| _version_ | 1832590127873916928 |
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| author | Ryusuke Kon |
| author_facet | Ryusuke Kon |
| author_sort | Ryusuke Kon |
| collection | DOAJ |
| description | The concept of limiting factors (or regulating factors) succeeded in formulating the well-known principle of competitive exclusion.This paper shows that the concept of limiting factors is helpful not only to formulate the competitive exclusion principle, but also to obtain other ecological insights.To this end, by focusing on a specific community structure, we study the dynamics of Kolmogorov equations and show that it is possible to derive an ecologically insightful result only from the information about interactions between species and limiting factors.Furthermore, we find that the derived result is a generalization of the preceding work by Shigesada, Kawasaki, and Teramoto (1984), who examined a certain Lotka-Volterra equation in a different context. |
| format | Article |
| id | doaj-art-83ac7804eebf4013984ee0ee09530c08 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2014-11-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-83ac7804eebf4013984ee0ee09530c082025-01-24T02:31:27ZengAIMS PressMathematical Biosciences and Engineering1551-00182014-11-01121718110.3934/mbe.2015.12.71Dynamics of competitive systems with a single common limiting factorRyusuke Kon0Faculty of Engineering, University of Miyazaki, Gakuen Kibanadai Nishi 1-1, Miyazaki 889-2192The concept of limiting factors (or regulating factors) succeeded in formulating the well-known principle of competitive exclusion.This paper shows that the concept of limiting factors is helpful not only to formulate the competitive exclusion principle, but also to obtain other ecological insights.To this end, by focusing on a specific community structure, we study the dynamics of Kolmogorov equations and show that it is possible to derive an ecologically insightful result only from the information about interactions between species and limiting factors.Furthermore, we find that the derived result is a generalization of the preceding work by Shigesada, Kawasaki, and Teramoto (1984), who examined a certain Lotka-Volterra equation in a different context.https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.71nonlinear complementary problemsaturated equilibriumlotka-volterra equation.p-functionp-matrix |
| spellingShingle | Ryusuke Kon Dynamics of competitive systems with a single common limiting factor Mathematical Biosciences and Engineering nonlinear complementary problem saturated equilibrium lotka-volterra equation. p-function p-matrix |
| title | Dynamics of competitive systems with a single common limiting factor |
| title_full | Dynamics of competitive systems with a single common limiting factor |
| title_fullStr | Dynamics of competitive systems with a single common limiting factor |
| title_full_unstemmed | Dynamics of competitive systems with a single common limiting factor |
| title_short | Dynamics of competitive systems with a single common limiting factor |
| title_sort | dynamics of competitive systems with a single common limiting factor |
| topic | nonlinear complementary problem saturated equilibrium lotka-volterra equation. p-function p-matrix |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.71 |
| work_keys_str_mv | AT ryusukekon dynamicsofcompetitivesystemswithasinglecommonlimitingfactor |