Dynamics Induced by Delay in a Nutrient-Phytoplankton Model with Multiple Delays
A nutrient-phytoplankton model with multiple delays is studied analytically and numerically. The aim of this paper is to study how the delay factors influence dynamics of interaction between nutrient and phytoplankton. The analytical analysis indicates that the positive equilibrium is always globall...
Saved in:
| Main Authors: | , , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2019-01-01
|
| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2019/3879626 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849305874992988160 |
|---|---|
| author | Chuanjun Dai Hengguo Yu Qing Guo He Liu Qi Wang Zengling Ma Min Zhao |
| author_facet | Chuanjun Dai Hengguo Yu Qing Guo He Liu Qi Wang Zengling Ma Min Zhao |
| author_sort | Chuanjun Dai |
| collection | DOAJ |
| description | A nutrient-phytoplankton model with multiple delays is studied analytically and numerically. The aim of this paper is to study how the delay factors influence dynamics of interaction between nutrient and phytoplankton. The analytical analysis indicates that the positive equilibrium is always globally asymptotically stable when the delay does not exist. On the contrary, the positive equilibrium loses its stability via Hopf instability induced by delay and then the corresponding periodic solutions emerge. Especially, the stability switches for positive equilibrium occur as the delay is increased. Furthermore, the numerical simulations show that periodic-2 and periodic-3 solutions can appear due to the existence of delays. Numerical results are consistent with the analytical results. Our results demonstrate that the delay has a great impact on the nutrient-phytoplankton dynamics. |
| format | Article |
| id | doaj-art-2f7e86d3cdab41de90398a9f87066e5b |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-2f7e86d3cdab41de90398a9f87066e5b2025-08-20T03:55:16ZengWileyComplexity1076-27871099-05262019-01-01201910.1155/2019/38796263879626Dynamics Induced by Delay in a Nutrient-Phytoplankton Model with Multiple DelaysChuanjun Dai0Hengguo Yu1Qing Guo2He Liu3Qi Wang4Zengling Ma5Min Zhao6Zhejiang Provincial Key Laboratory for Water Environment and Marine Biological Resources Protection, Wenzhou University, Wenzhou, Zhejiang, 325035, ChinaCollege of Mathematics, Physics and Electronic Information Engineering, Wenzhou University, Wenzhou, Zhejiang, 325035, ChinaEnvironmental Engineering Program, University of Northern British Columbia, Prince George, British Columbia, V2N 4Z9, CanadaEnvironmental Engineering Program, University of Northern British Columbia, Prince George, British Columbia, V2N 4Z9, CanadaZhejiang Provincial Key Laboratory for Water Environment and Marine Biological Resources Protection, Wenzhou University, Wenzhou, Zhejiang, 325035, ChinaZhejiang Provincial Key Laboratory for Water Environment and Marine Biological Resources Protection, Wenzhou University, Wenzhou, Zhejiang, 325035, ChinaZhejiang Provincial Key Laboratory for Water Environment and Marine Biological Resources Protection, Wenzhou University, Wenzhou, Zhejiang, 325035, ChinaA nutrient-phytoplankton model with multiple delays is studied analytically and numerically. The aim of this paper is to study how the delay factors influence dynamics of interaction between nutrient and phytoplankton. The analytical analysis indicates that the positive equilibrium is always globally asymptotically stable when the delay does not exist. On the contrary, the positive equilibrium loses its stability via Hopf instability induced by delay and then the corresponding periodic solutions emerge. Especially, the stability switches for positive equilibrium occur as the delay is increased. Furthermore, the numerical simulations show that periodic-2 and periodic-3 solutions can appear due to the existence of delays. Numerical results are consistent with the analytical results. Our results demonstrate that the delay has a great impact on the nutrient-phytoplankton dynamics.http://dx.doi.org/10.1155/2019/3879626 |
| spellingShingle | Chuanjun Dai Hengguo Yu Qing Guo He Liu Qi Wang Zengling Ma Min Zhao Dynamics Induced by Delay in a Nutrient-Phytoplankton Model with Multiple Delays Complexity |
| title | Dynamics Induced by Delay in a Nutrient-Phytoplankton Model with Multiple Delays |
| title_full | Dynamics Induced by Delay in a Nutrient-Phytoplankton Model with Multiple Delays |
| title_fullStr | Dynamics Induced by Delay in a Nutrient-Phytoplankton Model with Multiple Delays |
| title_full_unstemmed | Dynamics Induced by Delay in a Nutrient-Phytoplankton Model with Multiple Delays |
| title_short | Dynamics Induced by Delay in a Nutrient-Phytoplankton Model with Multiple Delays |
| title_sort | dynamics induced by delay in a nutrient phytoplankton model with multiple delays |
| url | http://dx.doi.org/10.1155/2019/3879626 |
| work_keys_str_mv | AT chuanjundai dynamicsinducedbydelayinanutrientphytoplanktonmodelwithmultipledelays AT hengguoyu dynamicsinducedbydelayinanutrientphytoplanktonmodelwithmultipledelays AT qingguo dynamicsinducedbydelayinanutrientphytoplanktonmodelwithmultipledelays AT heliu dynamicsinducedbydelayinanutrientphytoplanktonmodelwithmultipledelays AT qiwang dynamicsinducedbydelayinanutrientphytoplanktonmodelwithmultipledelays AT zenglingma dynamicsinducedbydelayinanutrientphytoplanktonmodelwithmultipledelays AT minzhao dynamicsinducedbydelayinanutrientphytoplanktonmodelwithmultipledelays |