Persistence of a competition model of plankton allelopathy in time–space periodic environment
This work is devoted to the study of a competition model of plankton allelopathy imposed in time-space periodic environment. We prove that the system admits positive periodic solutions under certain conditions. We further obtain some sufficient conditions for the uniqueness and global stability of t...
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| Published in | Nonlinear analysis: real world applications Vol. 79; p. 104136 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
01.10.2024
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| Abstract | This work is devoted to the study of a competition model of plankton allelopathy imposed in time-space periodic environment. We prove that the system admits positive periodic solutions under certain conditions. We further obtain some sufficient conditions for the uniqueness and global stability of the positive periodic solution, which shows that the model is persistent. The main tools for our arguments are comparison theorems based on the maximum principle, sub- and supersolutions method, and an iteration method, which also permit the treatment of some more general reaction–diffusion models in periodic environment. |
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| AbstractList | This work is devoted to the study of a competition model of plankton allelopathy imposed in time-space periodic environment. We prove that the system admits positive periodic solutions under certain conditions. We further obtain some sufficient conditions for the uniqueness and global stability of the positive periodic solution, which shows that the model is persistent. The main tools for our arguments are comparison theorems based on the maximum principle, sub- and supersolutions method, and an iteration method, which also permit the treatment of some more general reaction–diffusion models in periodic environment. |
| ArticleNumber | 104136 |
| Author | Du, Li-Jun Zhang, Li Cao, Qian |
| Author_xml | – sequence: 1 givenname: Li-Jun orcidid: 0000-0002-6476-6633 surname: Du fullname: Du, Li-Jun email: dulj20@chd.edu.cn – sequence: 2 givenname: Li surname: Zhang fullname: Zhang, Li – sequence: 3 givenname: Qian surname: Cao fullname: Cao, Qian |
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| Cites_doi | 10.1016/0362-546X(89)90054-0 10.1016/j.nonrwa.2007.01.001 10.1016/j.jde.2010.05.007 10.1016/j.nonrwa.2009.03.012 10.1016/0304-3800(94)00134-0 10.1016/j.nonrwa.2008.03.016 10.1016/j.nonrwa.2023.103866 10.1090/S0002-9947-1991-1028757-9 10.1016/j.jfa.2008.06.030 |
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| Keywords | Plankton allelopathy Stability Competition system Existence Uniqueness |
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| References | Nadin (b8) 2010; 249 Dancer (b2) 1991; 326 Maynard Smith (b3) 1974 Zhao (b10) 2003 Du (b12) 2023; 72 Tian, Zhang, Ling (b5) 2009; 10 Ahmad, Lazer (b1) 1989; 13 Chattopadhyay (b4) 1996; 84 Tian, Lin (b7) 2010; 3 Du, Bo (b11) 2023 Berestycki, Hamel, Nadin (b9) 2008; 255 Tian, Ling (b6) 2008; 9 Nadin (10.1016/j.nonrwa.2024.104136_b8) 2010; 249 Ahmad (10.1016/j.nonrwa.2024.104136_b1) 1989; 13 Dancer (10.1016/j.nonrwa.2024.104136_b2) 1991; 326 Tian (10.1016/j.nonrwa.2024.104136_b7) 2010; 3 Tian (10.1016/j.nonrwa.2024.104136_b5) 2009; 10 Maynard Smith (10.1016/j.nonrwa.2024.104136_b3) 1974 Zhao (10.1016/j.nonrwa.2024.104136_b10) 2003 Berestycki (10.1016/j.nonrwa.2024.104136_b9) 2008; 255 Chattopadhyay (10.1016/j.nonrwa.2024.104136_b4) 1996; 84 Tian (10.1016/j.nonrwa.2024.104136_b6) 2008; 9 Du (10.1016/j.nonrwa.2024.104136_b11) 2023 Du (10.1016/j.nonrwa.2024.104136_b12) 2023; 72 |
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| SubjectTerms | Competition system Existence Plankton allelopathy Stability Uniqueness |
| Title | Persistence of a competition model of plankton allelopathy in time–space periodic environment |
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