The Effect of Continuous and Pulse Input Nutrient on a Lake Model
In an aquatic environment, a mathematical model consisting of nutrient, phytoplankton, and zooplankton has been considered, where excretion of zooplankton is considered as one of the sources of nutrient. We investigate the effect of the input rate of the limiting nutrient from outside on controlling...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/462946 |
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| _version_ | 1832554077725130752 |
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| author | Yongfeng Li Dongliang Xie Jing-An Cui |
| author_facet | Yongfeng Li Dongliang Xie Jing-An Cui |
| author_sort | Yongfeng Li |
| collection | DOAJ |
| description | In an aquatic environment, a mathematical model consisting of nutrient, phytoplankton, and zooplankton has been considered, where excretion of zooplankton is considered as one of the sources of nutrient. We investigate the effect of the input rate of the limiting nutrient from outside on controlling algal bloom. First, we consider input limiting nutrient continuously, obtain the system has two boundary equilibria, and analyze the existence of the positive equilibrium by means of stability analysis, we get conditions for the stability of the equilibria. Then, we consider input limiting nutrient impulsively. We get the exact expression of the boundary periodic solution and obtain the condition for the stability of the periodic boundary solution. We also consider the effect of temperature on the system and give a model of Taihu Lake as an example. Finally, we give numerical simulation of our results and explain the effect of input limiting nutrient on controlling bloom of the lake system. |
| format | Article |
| id | doaj-art-3fd9a643c1f143fcade819c6524eb578 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-3fd9a643c1f143fcade819c6524eb5782025-02-03T05:52:20ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/462946462946The Effect of Continuous and Pulse Input Nutrient on a Lake ModelYongfeng Li0Dongliang Xie1Jing-An Cui2Department of Mathematics and Information Science, Zhengzhou University of Light Industry, Zhengzhou 450002, Henan, ChinaDepartment of Mathematics and Information Science, Zhengzhou University of Light Industry, Zhengzhou 450002, Henan, ChinaSchool of Science, Beijing University of Civil Engineering and Architecture, Beijing 100044, ChinaIn an aquatic environment, a mathematical model consisting of nutrient, phytoplankton, and zooplankton has been considered, where excretion of zooplankton is considered as one of the sources of nutrient. We investigate the effect of the input rate of the limiting nutrient from outside on controlling algal bloom. First, we consider input limiting nutrient continuously, obtain the system has two boundary equilibria, and analyze the existence of the positive equilibrium by means of stability analysis, we get conditions for the stability of the equilibria. Then, we consider input limiting nutrient impulsively. We get the exact expression of the boundary periodic solution and obtain the condition for the stability of the periodic boundary solution. We also consider the effect of temperature on the system and give a model of Taihu Lake as an example. Finally, we give numerical simulation of our results and explain the effect of input limiting nutrient on controlling bloom of the lake system.http://dx.doi.org/10.1155/2014/462946 |
| spellingShingle | Yongfeng Li Dongliang Xie Jing-An Cui The Effect of Continuous and Pulse Input Nutrient on a Lake Model Journal of Applied Mathematics |
| title | The Effect of Continuous and Pulse Input Nutrient on a Lake Model |
| title_full | The Effect of Continuous and Pulse Input Nutrient on a Lake Model |
| title_fullStr | The Effect of Continuous and Pulse Input Nutrient on a Lake Model |
| title_full_unstemmed | The Effect of Continuous and Pulse Input Nutrient on a Lake Model |
| title_short | The Effect of Continuous and Pulse Input Nutrient on a Lake Model |
| title_sort | effect of continuous and pulse input nutrient on a lake model |
| url | http://dx.doi.org/10.1155/2014/462946 |
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