Journal of the
Korean Mathematical Society JKMS

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

MSC numbers: 34K45, 34C25, 92D25