Stability and Hopf Bifurcation in a Three-Component Planktonic Model with Spatial Diffusion and Time Delay
Due to the different roles that nontoxic phytoplankton and toxin-producing phytoplankton play in the whole aquatic system, a delayed reaction-diffusion planktonic model under homogeneous Neumann boundary condition is investigated theoretically and numerically. This model describes the interactions b...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2019/4590915 |
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| _version_ | 1832554133703360512 |
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| author | Kejun Zhuang Gao Jia Dezhi Liu |
| author_facet | Kejun Zhuang Gao Jia Dezhi Liu |
| author_sort | Kejun Zhuang |
| collection | DOAJ |
| description | Due to the different roles that nontoxic phytoplankton and toxin-producing phytoplankton play in the whole aquatic system, a delayed reaction-diffusion planktonic model under homogeneous Neumann boundary condition is investigated theoretically and numerically. This model describes the interactions between the zooplankton and two kinds of phytoplanktons. The long-time behavior of the model and existence of positive constant equilibrium solution are first discussed. Then, the stability of constant equilibrium solution and occurrence of Hopf bifurcation are detailed and analyzed by using the bifurcation theory. Moreover, the formulas for determining the bifurcation direction and stability of spatially bifurcating solutions are derived. Finally, some numerical simulations are performed to verify the appearance of the spatially homogeneous and nonhomogeneous periodic solutions. |
| format | Article |
| id | doaj-art-1a593697de20469e94550301f6b755f1 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-1a593697de20469e94550301f6b755f12025-02-03T05:52:13ZengWileyComplexity1076-27871099-05262019-01-01201910.1155/2019/45909154590915Stability and Hopf Bifurcation in a Three-Component Planktonic Model with Spatial Diffusion and Time DelayKejun Zhuang0Gao Jia1Dezhi Liu2School of Statistics and Applied Mathematics, Anhui University of Finance and Economics, Bengbu 233030, ChinaCollege of Science, University of Shanghai for Science and Technology, Shanghai 200093, ChinaSchool of Statistics and Applied Mathematics, Anhui University of Finance and Economics, Bengbu 233030, ChinaDue to the different roles that nontoxic phytoplankton and toxin-producing phytoplankton play in the whole aquatic system, a delayed reaction-diffusion planktonic model under homogeneous Neumann boundary condition is investigated theoretically and numerically. This model describes the interactions between the zooplankton and two kinds of phytoplanktons. The long-time behavior of the model and existence of positive constant equilibrium solution are first discussed. Then, the stability of constant equilibrium solution and occurrence of Hopf bifurcation are detailed and analyzed by using the bifurcation theory. Moreover, the formulas for determining the bifurcation direction and stability of spatially bifurcating solutions are derived. Finally, some numerical simulations are performed to verify the appearance of the spatially homogeneous and nonhomogeneous periodic solutions.http://dx.doi.org/10.1155/2019/4590915 |
| spellingShingle | Kejun Zhuang Gao Jia Dezhi Liu Stability and Hopf Bifurcation in a Three-Component Planktonic Model with Spatial Diffusion and Time Delay Complexity |
| title | Stability and Hopf Bifurcation in a Three-Component Planktonic Model with Spatial Diffusion and Time Delay |
| title_full | Stability and Hopf Bifurcation in a Three-Component Planktonic Model with Spatial Diffusion and Time Delay |
| title_fullStr | Stability and Hopf Bifurcation in a Three-Component Planktonic Model with Spatial Diffusion and Time Delay |
| title_full_unstemmed | Stability and Hopf Bifurcation in a Three-Component Planktonic Model with Spatial Diffusion and Time Delay |
| title_short | Stability and Hopf Bifurcation in a Three-Component Planktonic Model with Spatial Diffusion and Time Delay |
| title_sort | stability and hopf bifurcation in a three component planktonic model with spatial diffusion and time delay |
| url | http://dx.doi.org/10.1155/2019/4590915 |
| work_keys_str_mv | AT kejunzhuang stabilityandhopfbifurcationinathreecomponentplanktonicmodelwithspatialdiffusionandtimedelay AT gaojia stabilityandhopfbifurcationinathreecomponentplanktonicmodelwithspatialdiffusionandtimedelay AT dezhiliu stabilityandhopfbifurcationinathreecomponentplanktonicmodelwithspatialdiffusionandtimedelay |