Dynamics of a time-periodic and delayed reaction-diffusion model with a quiescent stage
In this paper, we study a time-periodic and delayed reaction-diffusion system with quiescent stage in both unbounded and bounded habitat domains. In unbounded habitat domain $\mathbb{R}$, we first prove the existence of the asymptotic spreading speed and then show that it coincides with the minimal...
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| Format: | Article |
| Language: | English |
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University of Szeged
2016-07-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=4414 |
| _version_ | 1797830570673176576 |
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| author | Shuang-Ming Wang Liang Zhang |
| author_facet | Shuang-Ming Wang Liang Zhang |
| author_sort | Shuang-Ming Wang |
| collection | DOAJ |
| description | In this paper, we study a time-periodic and delayed reaction-diffusion system with quiescent stage in both unbounded and bounded habitat domains. In unbounded habitat domain $\mathbb{R}$, we first prove the existence of the asymptotic spreading speed and then show that it coincides with the minimal wave speed for monotone periodic traveling waves. In a bounded habitat domain $\Omega\subset\mathbb{R}^N\ (N\geq1)$, we obtain the threshold result on the global attractivity of either the zero solution or the unique positive time-periodic solution of the system. |
| first_indexed | 2024-04-09T13:39:18Z |
| format | Article |
| id | doaj.art-46da569fbaf44995b6192f9275109672 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:39:18Z |
| publishDate | 2016-07-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-46da569fbaf44995b6192f92751096722023-05-09T07:53:05ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752016-07-0120164712510.14232/ejqtde.2016.1.474414Dynamics of a time-periodic and delayed reaction-diffusion model with a quiescent stageShuang-Ming Wang0Liang Zhang1Lanzhou University of Finance and Economics, Lanzhou, Gansu, ChinaLanzhou University, Lanzhou, Gansu, P.R. ChinaIn this paper, we study a time-periodic and delayed reaction-diffusion system with quiescent stage in both unbounded and bounded habitat domains. In unbounded habitat domain $\mathbb{R}$, we first prove the existence of the asymptotic spreading speed and then show that it coincides with the minimal wave speed for monotone periodic traveling waves. In a bounded habitat domain $\Omega\subset\mathbb{R}^N\ (N\geq1)$, we obtain the threshold result on the global attractivity of either the zero solution or the unique positive time-periodic solution of the system.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=4414quiescent stagetime-periodicdelayspreading speedglobal attractivity |
| spellingShingle | Shuang-Ming Wang Liang Zhang Dynamics of a time-periodic and delayed reaction-diffusion model with a quiescent stage Electronic Journal of Qualitative Theory of Differential Equations quiescent stage time-periodic delay spreading speed global attractivity |
| title | Dynamics of a time-periodic and delayed reaction-diffusion model with a quiescent stage |
| title_full | Dynamics of a time-periodic and delayed reaction-diffusion model with a quiescent stage |
| title_fullStr | Dynamics of a time-periodic and delayed reaction-diffusion model with a quiescent stage |
| title_full_unstemmed | Dynamics of a time-periodic and delayed reaction-diffusion model with a quiescent stage |
| title_short | Dynamics of a time-periodic and delayed reaction-diffusion model with a quiescent stage |
| title_sort | dynamics of a time periodic and delayed reaction diffusion model with a quiescent stage |
| topic | quiescent stage time-periodic delay spreading speed global attractivity |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=4414 |
| work_keys_str_mv | AT shuangmingwang dynamicsofatimeperiodicanddelayedreactiondiffusionmodelwithaquiescentstage AT liangzhang dynamicsofatimeperiodicanddelayedreactiondiffusionmodelwithaquiescentstage |