Stability Switches and Hopf Bifurcation Induced by Nutrient Recycling Delay in a Reaction-Diffusion Nutrient-Phytoplankton Model
In this paper, we study a reaction-diffusion nutrient-phytoplankton model with nutrient recycling delay and toxin-producing phytoplankton. For the delay-free case, we prove that the release rate of toxic chemicals by the toxin-producing phytoplankton can destabilize the system and cause periodic osc...
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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/10.1155/2021/7943788 |
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| _version_ | 1832548924784640000 |
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| author | Kejun Zhuang Ying Li Bin Gong |
| author_facet | Kejun Zhuang Ying Li Bin Gong |
| author_sort | Kejun Zhuang |
| collection | DOAJ |
| description | In this paper, we study a reaction-diffusion nutrient-phytoplankton model with nutrient recycling delay and toxin-producing phytoplankton. For the delay-free case, we prove that the release rate of toxic chemicals by the toxin-producing phytoplankton can destabilize the system and cause periodic oscillation. For the time-delayed case, we observe that nutrient recycling delay may bring about stability switches and Hopf bifurcation. Moreover, we derive the formula for determining the direction and stability of the bifurcating periodic solutions. Finally, we give some numerical simulations to support the theoretical analyses. |
| format | Article |
| id | doaj-art-e0dce33bfdd34bfba14eba42a6f78d61 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-e0dce33bfdd34bfba14eba42a6f78d612025-02-03T06:12:48ZengWileyComplexity1076-27871099-05262021-01-01202110.1155/2021/79437887943788Stability Switches and Hopf Bifurcation Induced by Nutrient Recycling Delay in a Reaction-Diffusion Nutrient-Phytoplankton ModelKejun Zhuang0Ying Li1Bin Gong2School of Statistics and Applied Mathematics, Anhui University of Finance and Economics, Bengbu 233030, ChinaSchool of Statistics and Applied Mathematics, Anhui University of Finance and Economics, Bengbu 233030, ChinaExperiment and Practical Teaching Center, Anhui University of Finance and Economics, Bengbu 233030, ChinaIn this paper, we study a reaction-diffusion nutrient-phytoplankton model with nutrient recycling delay and toxin-producing phytoplankton. For the delay-free case, we prove that the release rate of toxic chemicals by the toxin-producing phytoplankton can destabilize the system and cause periodic oscillation. For the time-delayed case, we observe that nutrient recycling delay may bring about stability switches and Hopf bifurcation. Moreover, we derive the formula for determining the direction and stability of the bifurcating periodic solutions. Finally, we give some numerical simulations to support the theoretical analyses.http://dx.doi.org/10.1155/2021/7943788 |
| spellingShingle | Kejun Zhuang Ying Li Bin Gong Stability Switches and Hopf Bifurcation Induced by Nutrient Recycling Delay in a Reaction-Diffusion Nutrient-Phytoplankton Model Complexity |
| title | Stability Switches and Hopf Bifurcation Induced by Nutrient Recycling Delay in a Reaction-Diffusion Nutrient-Phytoplankton Model |
| title_full | Stability Switches and Hopf Bifurcation Induced by Nutrient Recycling Delay in a Reaction-Diffusion Nutrient-Phytoplankton Model |
| title_fullStr | Stability Switches and Hopf Bifurcation Induced by Nutrient Recycling Delay in a Reaction-Diffusion Nutrient-Phytoplankton Model |
| title_full_unstemmed | Stability Switches and Hopf Bifurcation Induced by Nutrient Recycling Delay in a Reaction-Diffusion Nutrient-Phytoplankton Model |
| title_short | Stability Switches and Hopf Bifurcation Induced by Nutrient Recycling Delay in a Reaction-Diffusion Nutrient-Phytoplankton Model |
| title_sort | stability switches and hopf bifurcation induced by nutrient recycling delay in a reaction diffusion nutrient phytoplankton model |
| url | http://dx.doi.org/10.1155/2021/7943788 |
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