Dynamical analysis of a Lotka Volterra commensalism model with additive Allee effect
We propose and analyze a Lotka-Volterra commensal model with an additive Allee effect in this article. First, we study the existence and local stability of possible equilibria. Second, the conditions for the existence of saddle-node bifurcations and transcritical bifurcations are derived by using So...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2022-08-01
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| Series: | Open Mathematics |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/math-2022-0055 |
| _version_ | 1818025224230141952 |
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| author | He Xiaqing Zhu Zhenliang Chen Jialin Chen Fengde |
| author_facet | He Xiaqing Zhu Zhenliang Chen Jialin Chen Fengde |
| author_sort | He Xiaqing |
| collection | DOAJ |
| description | We propose and analyze a Lotka-Volterra commensal model with an additive Allee effect in this article. First, we study the existence and local stability of possible equilibria. Second, the conditions for the existence of saddle-node bifurcations and transcritical bifurcations are derived by using Sotomayor’s theorem. Third, we give sufficient conditions for the global stability of the boundary equilibrium and positive equilibrium. Finally, we use numerical simulations to verify the above theoretical results. This study shows that for the weak Allee effect case, the additive Allee effect has a negative effect on the final density of both species, with increasing Allee effect, the densities of both species are decreasing. For the strong Allee effect case, the additive Allee effect is one of the most important factors that leads to the extinction of the second species. The additive Allee effect leads to the complex dynamic behaviors of the system. |
| first_indexed | 2024-12-10T04:12:42Z |
| format | Article |
| id | doaj.art-ce66de93640e4d70af2a80419ff2a8ca |
| institution | Directory Open Access Journal |
| issn | 2391-5455 |
| language | English |
| last_indexed | 2024-12-10T04:12:42Z |
| publishDate | 2022-08-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj.art-ce66de93640e4d70af2a80419ff2a8ca2022-12-22T02:02:41ZengDe GruyterOpen Mathematics2391-54552022-08-0120164666510.1515/math-2022-0055Dynamical analysis of a Lotka Volterra commensalism model with additive Allee effectHe Xiaqing0Zhu Zhenliang1Chen Jialin2Chen Fengde3School of Mathematics and Statistics, Fuzhou University, Fuzhou, Fujian 350108, ChinaCollege of Mathematics and Data Science, Minjiang University, Fuzhou, ChinaSchool of Mathematics and Statistics, Fuzhou University, Fuzhou, Fujian 350108, ChinaSchool of Mathematics and Statistics, Fuzhou University, Fuzhou, Fujian 350108, ChinaWe propose and analyze a Lotka-Volterra commensal model with an additive Allee effect in this article. First, we study the existence and local stability of possible equilibria. Second, the conditions for the existence of saddle-node bifurcations and transcritical bifurcations are derived by using Sotomayor’s theorem. Third, we give sufficient conditions for the global stability of the boundary equilibrium and positive equilibrium. Finally, we use numerical simulations to verify the above theoretical results. This study shows that for the weak Allee effect case, the additive Allee effect has a negative effect on the final density of both species, with increasing Allee effect, the densities of both species are decreasing. For the strong Allee effect case, the additive Allee effect is one of the most important factors that leads to the extinction of the second species. The additive Allee effect leads to the complex dynamic behaviors of the system.https://doi.org/10.1515/math-2022-0055lotka-volterra commensal modeladditive allee effectbifurcation92d2534d20 |
| spellingShingle | He Xiaqing Zhu Zhenliang Chen Jialin Chen Fengde Dynamical analysis of a Lotka Volterra commensalism model with additive Allee effect Open Mathematics lotka-volterra commensal model additive allee effect bifurcation 92d25 34d20 |
| title | Dynamical analysis of a Lotka Volterra commensalism model with additive Allee effect |
| title_full | Dynamical analysis of a Lotka Volterra commensalism model with additive Allee effect |
| title_fullStr | Dynamical analysis of a Lotka Volterra commensalism model with additive Allee effect |
| title_full_unstemmed | Dynamical analysis of a Lotka Volterra commensalism model with additive Allee effect |
| title_short | Dynamical analysis of a Lotka Volterra commensalism model with additive Allee effect |
| title_sort | dynamical analysis of a lotka volterra commensalism model with additive allee effect |
| topic | lotka-volterra commensal model additive allee effect bifurcation 92d25 34d20 |
| url | https://doi.org/10.1515/math-2022-0055 |
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