Journal Article

Extinction and permanence of a two‐prey one‐predator system with impulsive effect

Yujuan Zhang, Bing Liu and Lansun Chen

in Mathematical Medicine and Biology: A Journal of the IMA

Published on behalf of Institute of Mathematics and its Applications

Volume 20, issue 4, pages 309-325
Published in print December 2003 | ISSN: 1477-8599
Published online December 2003 | e-ISSN: 1477-8602 | DOI: http://dx.doi.org/10.1093/imammb/20.4.309
Extinction and permanence of a two‐prey one‐predator system with impulsive effect

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In this paper, we investigate a two‐prey one‐predator system with impulsive effect on the predator of fixed moment. By using Floquet's theorem and small‐amplitude perturbation skills, we show that there exists a globally asymptotically stable two‐pest eradication periodic solution when the impulsive period is less than some critical value. Further, we prove that the system is permanent if the impulsive period is larger than some critical value, and meanwhile the conditions for the extinction of one of the two prey and permanence of the remaining two species are given. Finally, numerical simulation shows that there exists a stable positive periodic solution with a maximum value no larger than a given level. Therefore, we can use the stability of the positive periodic solution and its period to control insect pests at acceptably low levels.

Keywords: two‐prey one‐predator system; impulsive effect; permanence; extinction

Journal Article.  0 words. 

Subjects: Applied Mathematics ; Biomathematics and Statistics

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