## Journal of Applied Mathematics

### Dynamics of a Stage Structured Pest Control Model in a Polluted Environment with Pulse Pollution Input

#### Abstract

By using pollution model and impulsive delay differential equation, we formulate a pest control model with stage structure for natural enemy in a polluted environment by introducing a constant periodic pollutant input and killing pest at different fixed moments and investigate the dynamics of such a system. We assume only that the natural enemies are affected by pollution, and we choose the method to kill the pest without harming natural enemies. Sufficient conditions for global attractivity of the natural enemy-extinction periodic solution and permanence of the system are obtained. Numerical simulations are presented to confirm our theoretical results.

#### Article information

Source
J. Appl. Math., Volume 2013 (2013), Article ID 678762, 8 pages.

Dates
First available in Project Euclid: 14 March 2014

https://projecteuclid.org/euclid.jam/1394808171

Digital Object Identifier
doi:10.1155/2013/678762

Mathematical Reviews number (MathSciNet)
MR3122117

Zentralblatt MATH identifier
06950816

#### Citation

Liu, Bing; Xu, Ling; Kang, Baolin. Dynamics of a Stage Structured Pest Control Model in a Polluted Environment with Pulse Pollution Input. J. Appl. Math. 2013 (2013), Article ID 678762, 8 pages. doi:10.1155/2013/678762. https://projecteuclid.org/euclid.jam/1394808171

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