Mathematical analysis on deterministic and stochastic lake ecosystem models
In this paper, we propose and study the deterministic and stochastic lake ecosystem models to investigate the impact of terrestrial organic matter upon persistence of the plankton populations. By constructing Lyapunov function and using the LaSalle's Invariance Principle, we establish global pr...
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| Format: | Article |
| Language: | English |
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AIMS Press
2019-05-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/10.3934/mbe.2019237?viewType=HTML |
| _version_ | 1818356896845791232 |
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| author | Zhiwei Huang Gang Huang |
| author_facet | Zhiwei Huang Gang Huang |
| author_sort | Zhiwei Huang |
| collection | DOAJ |
| description | In this paper, we propose and study the deterministic and stochastic lake ecosystem models to investigate the impact of terrestrial organic matter upon persistence of the plankton populations. By constructing Lyapunov function and using the LaSalle's Invariance Principle, we establish global properties of the deterministic model. The dynamical behavior of solutions fits well with some experimental results. It is concluded that the terrestrial organic matter plays an important role in influencing interactions between phytoplankton and zooplankton. Based on the fluctuations of lake ecosystem, we further develop a stochastically perturbed model. Theoretic analysis implies that the stochastic model exists a stationary distribution which is ergodic. The key point of our analysis is to enhance our knowledge of the factors governing the dynamics of plankton population models. |
| first_indexed | 2024-12-13T20:04:30Z |
| format | Article |
| id | doaj.art-b91d9fa739a540f9a104329300e5065b |
| institution | Directory Open Access Journal |
| issn | 1551-0018 |
| language | English |
| last_indexed | 2024-12-13T20:04:30Z |
| publishDate | 2019-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj.art-b91d9fa739a540f9a104329300e5065b2022-12-21T23:33:04ZengAIMS PressMathematical Biosciences and Engineering1551-00182019-05-011654723474010.3934/mbe.2019237Mathematical analysis on deterministic and stochastic lake ecosystem modelsZhiwei Huang0Gang Huang 1School of Mathematics and Physics, China University of Geosciences, 430074, Wuhan, P.R. ChinaSchool of Mathematics and Physics, China University of Geosciences, 430074, Wuhan, P.R. ChinaIn this paper, we propose and study the deterministic and stochastic lake ecosystem models to investigate the impact of terrestrial organic matter upon persistence of the plankton populations. By constructing Lyapunov function and using the LaSalle's Invariance Principle, we establish global properties of the deterministic model. The dynamical behavior of solutions fits well with some experimental results. It is concluded that the terrestrial organic matter plays an important role in influencing interactions between phytoplankton and zooplankton. Based on the fluctuations of lake ecosystem, we further develop a stochastically perturbed model. Theoretic analysis implies that the stochastic model exists a stationary distribution which is ergodic. The key point of our analysis is to enhance our knowledge of the factors governing the dynamics of plankton population models.https://www.aimspress.com/article/10.3934/mbe.2019237?viewType=HTMLterrestrial organic matterlyapunov functionitô’s formulastationary distribution |
| spellingShingle | Zhiwei Huang Gang Huang Mathematical analysis on deterministic and stochastic lake ecosystem models Mathematical Biosciences and Engineering terrestrial organic matter lyapunov function itô’s formula stationary distribution |
| title | Mathematical analysis on deterministic and stochastic lake ecosystem models |
| title_full | Mathematical analysis on deterministic and stochastic lake ecosystem models |
| title_fullStr | Mathematical analysis on deterministic and stochastic lake ecosystem models |
| title_full_unstemmed | Mathematical analysis on deterministic and stochastic lake ecosystem models |
| title_short | Mathematical analysis on deterministic and stochastic lake ecosystem models |
| title_sort | mathematical analysis on deterministic and stochastic lake ecosystem models |
| topic | terrestrial organic matter lyapunov function itô’s formula stationary distribution |
| url | https://www.aimspress.com/article/10.3934/mbe.2019237?viewType=HTML |
| work_keys_str_mv | AT zhiweihuang mathematicalanalysisondeterministicandstochasticlakeecosystemmodels AT ganghuang mathematicalanalysisondeterministicandstochasticlakeecosystemmodels |