Bifurcation analysis of a diffusive plant-wrack model with tide effect on the wrack
This paper deals with the spatial, temporal and spatiotemporal dynamics of a spatial plant-wrack model. The parameter regions for the stability and instability of the unique positive constant steady state solution are derived, and the existence of time-periodic orbits and non-constant steady state s...
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| Format: | Article |
| Language: | English |
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AIMS Press
2016-04-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2016021 |
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| _version_ | 1832590061521076224 |
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| author | Jun Zhou |
| author_facet | Jun Zhou |
| author_sort | Jun Zhou |
| collection | DOAJ |
| description | This paper deals with the spatial, temporal and spatiotemporal dynamics of a spatial plant-wrack model. The parameter regions for the stability and instability of the unique positive constant steady state solution are derived, and the existence of time-periodic orbits and non-constant steady state solutions are proved by bifurcation method. The nonexistence of positive nonconstant steady state solutions are studied by energy method and Implicit Function Theorem. Numerical simulations are presented to verify and illustrate the theoretical results. |
| format | Article |
| id | doaj-art-84c1daf91a58489db58f4880f918b190 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2016-04-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-84c1daf91a58489db58f4880f918b1902025-01-24T02:36:35ZengAIMS PressMathematical Biosciences and Engineering1551-00182016-04-0113485788510.3934/mbe.2016021Bifurcation analysis of a diffusive plant-wrack model with tide effect on the wrackJun Zhou0School of Mathematics and Statistics, Southwest University, Chongqing, 400715This paper deals with the spatial, temporal and spatiotemporal dynamics of a spatial plant-wrack model. The parameter regions for the stability and instability of the unique positive constant steady state solution are derived, and the existence of time-periodic orbits and non-constant steady state solutions are proved by bifurcation method. The nonexistence of positive nonconstant steady state solutions are studied by energy method and Implicit Function Theorem. Numerical simulations are presented to verify and illustrate the theoretical results.https://www.aimspress.com/article/doi/10.3934/mbe.2016021steady-state bifurcationplant-wrack modelstabilityhopf bifurcationnonconstant positive solutions.turing instability |
| spellingShingle | Jun Zhou Bifurcation analysis of a diffusive plant-wrack model with tide effect on the wrack Mathematical Biosciences and Engineering steady-state bifurcation plant-wrack model stability hopf bifurcation nonconstant positive solutions. turing instability |
| title | Bifurcation analysis of a diffusive plant-wrack model with tide effect on the wrack |
| title_full | Bifurcation analysis of a diffusive plant-wrack model with tide effect on the wrack |
| title_fullStr | Bifurcation analysis of a diffusive plant-wrack model with tide effect on the wrack |
| title_full_unstemmed | Bifurcation analysis of a diffusive plant-wrack model with tide effect on the wrack |
| title_short | Bifurcation analysis of a diffusive plant-wrack model with tide effect on the wrack |
| title_sort | bifurcation analysis of a diffusive plant wrack model with tide effect on the wrack |
| topic | steady-state bifurcation plant-wrack model stability hopf bifurcation nonconstant positive solutions. turing instability |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2016021 |
| work_keys_str_mv | AT junzhou bifurcationanalysisofadiffusiveplantwrackmodelwithtideeffectonthewrack |