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http://dx.doi.org/10.4134/JKMS.2009.46.1.071

ANALYSIS OF A STAGE-STRUCTURED PREDATOR-PREY SYSTEM WITH IMPULSIVE PERTURBATIONS AND TIME DELAYS  

Song, Xinyu (COLLEGE OF MATHEMATICS AND INFORMATION SCIENCE XINYANG NORMAL UNIVERSITY)
Li, Senlin (COLLEGE OF MATHEMATICS AND INFORMATION SCIENCE XINYANG NORMAL UNIVERSITY)
Li, An (COLLEGE OF MATHEMATICAL SCIENCES XIAMEN UNIVERSITY)
Publication Information
Journal of the Korean Mathematical Society / v.46, no.1, 2009 , pp. 71-82 More about this Journal
Abstract
In this paper, a stage-structured predator-prey system with impulsive perturbations and time delays is presented to investigate the ecological problem of how a pest population and natural enemy population can coexist. Sufficient conditions are obtained using a discrete dynamical system determined by a stroboscopic map, which guarantee that a 'predator-extinction' periodic solution is globally attractive. When the impulsive period is longer than some time threshold or the impulsive harvesting rate is below a control threshold, the system is permanent. Our results provide some reasonable suggestions for pest management.
Keywords
stage-structured; time delay; impulsive perturbations; globally asymptotic stability;
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