Modeling the Dynamics of a Single-Species Model with Pollution Treatment in a Polluted Environment. (7th February 2013)

• Record Type: Journal Article
• Authors: Liu, Bing; Luan, Shi; Gao, Yinghui
• Other Names: Jin Zhen Academic Editor.
• Is Part Of: Discrete dynamics in nature and society. Volume 2013(2013)
• Publication Date: 2013-02-07
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/2013/412409
• Languages: English
• ISSNs: 1026-0226

Abstract

Abstract : 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.