Modeling the dynamics of a single-species model with pollution treatment in a polluted environment
type: Item
instance of: scholarly article
title: Modeling the dynamics of a single-species model with pollution treatment in a polluted environment
zbMATH Open document ID: 1264.34161
DOI: 10.1155/2013/412409
author: Bing Liu
author: Shi Luan
author: Yinghui Gao
published in: Discrete Dynamics in Nature and Society
publication date: 2013-06-13T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 34K60
Mathematics Subject Classification ID: 92D40
Mathematics Subject Classification ID: 65L99
zbMATH DE Number: 6175078
Wikidata QID: Q58921574
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/412409
OpenAlex ID: W2001509763
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description: scientific article; zbMATH DE number 6175078