Dynamic behaviors of a Leslie-Gower predator-prey model with Smith growth and constant-yield harvesting
A Leslie-Gower predator-prey model with Smith growth and constant-yield harvesting is proposed in this paper. We show that the system admits at most two boundary equilibria, both of which are unstable. The degenerate positive equilibrium of the system is a cusp of codimension 2, and the system under...
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AIMS Press
2024-11-01
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2024299 |
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| author | Mengxin He Zhong Li |
| author_facet | Mengxin He Zhong Li |
| author_sort | Mengxin He |
| collection | DOAJ |
| description | A Leslie-Gower predator-prey model with Smith growth and constant-yield harvesting is proposed in this paper. We show that the system admits at most two boundary equilibria, both of which are unstable. The degenerate positive equilibrium of the system is a cusp of codimension 2, and the system undergoes cusp-type Bogdanov-Takens bifurcation of codimension 2. Moreover, we prove that the system has a weak focus of order at most 3, and the system can undergo a degenerate Hopf bifurcation of codimension 3. Our results reveal that the constant-yield harvesting can lead to richer dynamic behaviors. |
| format | Article |
| id | doaj-art-b93726ac62c546bd8742e4b33192091e |
| institution | Kabale University |
| issn | 2688-1594 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Electronic Research Archive |
| spelling | doaj-art-b93726ac62c546bd8742e4b33192091e2025-01-23T07:53:01ZengAIMS PressElectronic Research Archive2688-15942024-11-0132116424644210.3934/era.2024299Dynamic behaviors of a Leslie-Gower predator-prey model with Smith growth and constant-yield harvestingMengxin He0Zhong Li1School of Computer and Big Data, Minjiang University, Fuzhou, Fujian 350108, ChinaSchool of Mathematics and Statistics, Fuzhou University, Fuzhou, Fujian 350108, ChinaA Leslie-Gower predator-prey model with Smith growth and constant-yield harvesting is proposed in this paper. We show that the system admits at most two boundary equilibria, both of which are unstable. The degenerate positive equilibrium of the system is a cusp of codimension 2, and the system undergoes cusp-type Bogdanov-Takens bifurcation of codimension 2. Moreover, we prove that the system has a weak focus of order at most 3, and the system can undergo a degenerate Hopf bifurcation of codimension 3. Our results reveal that the constant-yield harvesting can lead to richer dynamic behaviors.https://www.aimspress.com/article/doi/10.3934/era.2024299leslie-gowerharvestinghopf bifurcationbogdanov-takens bifurcationsmith growth |
| spellingShingle | Mengxin He Zhong Li Dynamic behaviors of a Leslie-Gower predator-prey model with Smith growth and constant-yield harvesting Electronic Research Archive leslie-gower harvesting hopf bifurcation bogdanov-takens bifurcation smith growth |
| title | Dynamic behaviors of a Leslie-Gower predator-prey model with Smith growth and constant-yield harvesting |
| title_full | Dynamic behaviors of a Leslie-Gower predator-prey model with Smith growth and constant-yield harvesting |
| title_fullStr | Dynamic behaviors of a Leslie-Gower predator-prey model with Smith growth and constant-yield harvesting |
| title_full_unstemmed | Dynamic behaviors of a Leslie-Gower predator-prey model with Smith growth and constant-yield harvesting |
| title_short | Dynamic behaviors of a Leslie-Gower predator-prey model with Smith growth and constant-yield harvesting |
| title_sort | dynamic behaviors of a leslie gower predator prey model with smith growth and constant yield harvesting |
| topic | leslie-gower harvesting hopf bifurcation bogdanov-takens bifurcation smith growth |
| url | https://www.aimspress.com/article/doi/10.3934/era.2024299 |
| work_keys_str_mv | AT mengxinhe dynamicbehaviorsofalesliegowerpredatorpreymodelwithsmithgrowthandconstantyieldharvesting AT zhongli dynamicbehaviorsofalesliegowerpredatorpreymodelwithsmithgrowthandconstantyieldharvesting |