Stability and Bifurcation for a Delayed Diffusive Two-Zooplankton One-Phytoplankton Model with Two Different Functions
In this paper, a diffusion two-phytoplankton one-zooplankton model with time delay, Beddington–DeAnglis functional response, and Holling II functional response is proposed. First, the existence and local stability of all equilibria of such model are studied. Then, the existence of Hopf bifurcation o...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2021/5560157 |
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| author | Xin-You Meng Li Xiao |
| author_facet | Xin-You Meng Li Xiao |
| author_sort | Xin-You Meng |
| collection | DOAJ |
| description | In this paper, a diffusion two-phytoplankton one-zooplankton model with time delay, Beddington–DeAnglis functional response, and Holling II functional response is proposed. First, the existence and local stability of all equilibria of such model are studied. Then, the existence of Hopf bifurcation of the corresponding model without diffusion is given by taking time delay as the bifurcation parameter. Next, the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are investigated by using the normal form theory and center manifold theorem. Furthermore, due to the local bifurcation theory of partial functional differential equations, Hopf bifurcation of the model is investigated by considering time delay as the bifurcation parameter. The explicit formulas to determine the properties of Hopf bifurcation are given by the method of the normal form theory and center manifold theorem for partial functional differential equations. Finally, some numerical simulations are performed to check out our theoretical results. |
| format | Article |
| id | doaj-art-17caddd44e2644ba875219bf6d147d8e |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-17caddd44e2644ba875219bf6d147d8e2025-02-03T06:12:51ZengWileyComplexity1076-27871099-05262021-01-01202110.1155/2021/55601575560157Stability and Bifurcation for a Delayed Diffusive Two-Zooplankton One-Phytoplankton Model with Two Different FunctionsXin-You Meng0Li Xiao1School of Science, Lanzhou University of Technology, Lanzhou, Gansu 730050, ChinaSchool of Science, Lanzhou University of Technology, Lanzhou, Gansu 730050, ChinaIn this paper, a diffusion two-phytoplankton one-zooplankton model with time delay, Beddington–DeAnglis functional response, and Holling II functional response is proposed. First, the existence and local stability of all equilibria of such model are studied. Then, the existence of Hopf bifurcation of the corresponding model without diffusion is given by taking time delay as the bifurcation parameter. Next, the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are investigated by using the normal form theory and center manifold theorem. Furthermore, due to the local bifurcation theory of partial functional differential equations, Hopf bifurcation of the model is investigated by considering time delay as the bifurcation parameter. The explicit formulas to determine the properties of Hopf bifurcation are given by the method of the normal form theory and center manifold theorem for partial functional differential equations. Finally, some numerical simulations are performed to check out our theoretical results.http://dx.doi.org/10.1155/2021/5560157 |
| spellingShingle | Xin-You Meng Li Xiao Stability and Bifurcation for a Delayed Diffusive Two-Zooplankton One-Phytoplankton Model with Two Different Functions Complexity |
| title | Stability and Bifurcation for a Delayed Diffusive Two-Zooplankton One-Phytoplankton Model with Two Different Functions |
| title_full | Stability and Bifurcation for a Delayed Diffusive Two-Zooplankton One-Phytoplankton Model with Two Different Functions |
| title_fullStr | Stability and Bifurcation for a Delayed Diffusive Two-Zooplankton One-Phytoplankton Model with Two Different Functions |
| title_full_unstemmed | Stability and Bifurcation for a Delayed Diffusive Two-Zooplankton One-Phytoplankton Model with Two Different Functions |
| title_short | Stability and Bifurcation for a Delayed Diffusive Two-Zooplankton One-Phytoplankton Model with Two Different Functions |
| title_sort | stability and bifurcation for a delayed diffusive two zooplankton one phytoplankton model with two different functions |
| url | http://dx.doi.org/10.1155/2021/5560157 |
| work_keys_str_mv | AT xinyoumeng stabilityandbifurcationforadelayeddiffusivetwozooplanktononephytoplanktonmodelwithtwodifferentfunctions AT lixiao stabilityandbifurcationforadelayeddiffusivetwozooplanktononephytoplanktonmodelwithtwodifferentfunctions |