Modeling the Dynamics of a Single-Species Model with Pollution Treatment in a Polluted Environment
Without any question, environmental pollution is the main cause for the species extinction in recent times. In this paper, based on impulsive differential equation, the dynamics of a single-species model with impulsive pollution treatment at fixed time in a polluted environment is considered, in whi...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2013/412409 |
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| _version_ | 1832548266392158208 |
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| author | Bing Liu Shi Luan Yinghui Gao |
| author_facet | Bing Liu Shi Luan Yinghui Gao |
| author_sort | Bing Liu |
| collection | DOAJ |
| description | Without any question, environmental pollution is the main cause
for the species extinction in recent times. In this paper, based
on impulsive differential equation, the dynamics of a
single-species model with impulsive pollution treatment at fixed
time in a polluted environment is considered, in which we assume
that the species is directly affected by the pollutants.
Sufficient conditions for permanence and extinction of the species
are given. The results show that the species is permanent when the
impulsive period is less than some critical value, otherwise the
species will be extinct. Although shortening the impulsive period
can protect the species from extinction, it is expensive. To see
how pollution treatment applications could be economical, we also
establish a hybrid impulsive model involving periodic pollution
treatment at fixed time with state-dependent pollution treatment
applied when the pollution concentration reaches the given
Environment Threshold (ET). It indicates that the hybrid method is
the most effective method to protect the species from extinction.
Numerical simulations confirm our theoretical results. |
| format | Article |
| id | doaj-art-6d774115151547ad975db0eff5f45b80 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-6d774115151547ad975db0eff5f45b802025-02-03T06:15:12ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2013-01-01201310.1155/2013/412409412409Modeling the Dynamics of a Single-Species Model with Pollution Treatment in a Polluted EnvironmentBing Liu0Shi Luan1Yinghui Gao2College of Mathematics and Information Science, Anshan Normal University, Anshan, Liaoning 114007, ChinaDepartment of Mathematics, Liaoning Normal University, Dalian, Liaoning 116029, ChinaDepartment of Mathematics, Beihang University, Beijing 100083, ChinaWithout any question, environmental pollution is the main cause for the species extinction in recent times. In this paper, based on impulsive differential equation, the dynamics of a single-species model with impulsive pollution treatment at fixed time in a polluted environment is considered, in which we assume that the species is directly affected by the pollutants. Sufficient conditions for permanence and extinction of the species are given. The results show that the species is permanent when the impulsive period is less than some critical value, otherwise the species will be extinct. Although shortening the impulsive period can protect the species from extinction, it is expensive. To see how pollution treatment applications could be economical, we also establish a hybrid impulsive model involving periodic pollution treatment at fixed time with state-dependent pollution treatment applied when the pollution concentration reaches the given Environment Threshold (ET). It indicates that the hybrid method is the most effective method to protect the species from extinction. Numerical simulations confirm our theoretical results.http://dx.doi.org/10.1155/2013/412409 |
| spellingShingle | Bing Liu Shi Luan Yinghui Gao Modeling the Dynamics of a Single-Species Model with Pollution Treatment in a Polluted Environment Discrete Dynamics in Nature and Society |
| title | Modeling the Dynamics of a Single-Species Model with Pollution Treatment in a Polluted Environment |
| title_full | Modeling the Dynamics of a Single-Species Model with Pollution Treatment in a Polluted Environment |
| title_fullStr | Modeling the Dynamics of a Single-Species Model with Pollution Treatment in a Polluted Environment |
| title_full_unstemmed | Modeling the Dynamics of a Single-Species Model with Pollution Treatment in a Polluted Environment |
| title_short | Modeling the Dynamics of a Single-Species Model with Pollution Treatment in a Polluted Environment |
| title_sort | modeling the dynamics of a single species model with pollution treatment in a polluted environment |
| url | http://dx.doi.org/10.1155/2013/412409 |
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