Complicate dynamical properties of a discrete slow-fast predator-prey model with ratio-dependent functional response
Abstract Using a semidiscretization method, we derive in this paper a discrete slow-fast predator-prey system with ratio-dependent functional response. First of all, a detailed study for the local stability of fixed points of the system is obtained by invoking an important lemma. In addition, by uti...
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2023-11-01
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| Series: | Scientific Reports |
| Online Access: | https://doi.org/10.1038/s41598-023-45861-2 |
| _version_ | 1827634844807462912 |
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| author | Xianyi Li Jiange Dong |
| author_facet | Xianyi Li Jiange Dong |
| author_sort | Xianyi Li |
| collection | DOAJ |
| description | Abstract Using a semidiscretization method, we derive in this paper a discrete slow-fast predator-prey system with ratio-dependent functional response. First of all, a detailed study for the local stability of fixed points of the system is obtained by invoking an important lemma. In addition, by utilizing the center manifold theorem and the bifurcation theory some sufficient conditions are obtained for the transcritical bifurcation and Neimark-Sacker bifurcation of this system to occur. Finally, with the use of Matlab software, numerical simulations are carried out to illustrate the corresponding theoretical results and reveal some new dynamics of the system. Our results clearly demonstrate that the system is very sensitive to its fast time scale parameter variable. |
| first_indexed | 2024-03-09T15:18:58Z |
| format | Article |
| id | doaj.art-df3fab19314a44219b5660a0541e65cb |
| institution | Directory Open Access Journal |
| issn | 2045-2322 |
| language | English |
| last_indexed | 2024-03-09T15:18:58Z |
| publishDate | 2023-11-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj.art-df3fab19314a44219b5660a0541e65cb2023-11-26T12:56:36ZengNature PortfolioScientific Reports2045-23222023-11-0113111310.1038/s41598-023-45861-2Complicate dynamical properties of a discrete slow-fast predator-prey model with ratio-dependent functional responseXianyi Li0Jiange Dong1Department of Big Data Science, School of Science, Zhejiang University of Science and TechnologyDepartment of Big Data Science, School of Science, Zhejiang University of Science and TechnologyAbstract Using a semidiscretization method, we derive in this paper a discrete slow-fast predator-prey system with ratio-dependent functional response. First of all, a detailed study for the local stability of fixed points of the system is obtained by invoking an important lemma. In addition, by utilizing the center manifold theorem and the bifurcation theory some sufficient conditions are obtained for the transcritical bifurcation and Neimark-Sacker bifurcation of this system to occur. Finally, with the use of Matlab software, numerical simulations are carried out to illustrate the corresponding theoretical results and reveal some new dynamics of the system. Our results clearly demonstrate that the system is very sensitive to its fast time scale parameter variable.https://doi.org/10.1038/s41598-023-45861-2 |
| spellingShingle | Xianyi Li Jiange Dong Complicate dynamical properties of a discrete slow-fast predator-prey model with ratio-dependent functional response Scientific Reports |
| title | Complicate dynamical properties of a discrete slow-fast predator-prey model with ratio-dependent functional response |
| title_full | Complicate dynamical properties of a discrete slow-fast predator-prey model with ratio-dependent functional response |
| title_fullStr | Complicate dynamical properties of a discrete slow-fast predator-prey model with ratio-dependent functional response |
| title_full_unstemmed | Complicate dynamical properties of a discrete slow-fast predator-prey model with ratio-dependent functional response |
| title_short | Complicate dynamical properties of a discrete slow-fast predator-prey model with ratio-dependent functional response |
| title_sort | complicate dynamical properties of a discrete slow fast predator prey model with ratio dependent functional response |
| url | https://doi.org/10.1038/s41598-023-45861-2 |
| work_keys_str_mv | AT xianyili complicatedynamicalpropertiesofadiscreteslowfastpredatorpreymodelwithratiodependentfunctionalresponse AT jiangedong complicatedynamicalpropertiesofadiscreteslowfastpredatorpreymodelwithratiodependentfunctionalresponse |