J. Korean Math. Soc. 2007; 44(2): 327-342
Printed March 1, 2007
Copyright © The Korean Mathematical Society.
Xinyu Song and Hongjian Guo
Xinyang Normal University, Xinyang Normal University
In this paper, a kind of pest-predator model with impulsive effect and infinite delay is considered by the method of chain transform. By using Floquet's theorem, it is shown that there exists a globally asymptotically stable periodic pest eradication solution when the impulsive period is less than or equal to some critical value which is a directly proportional function with respect to the population of release. Furthermore, it is proved that the system is permanent if the impulsive period is larger than some critical value. Finally, the results of the corresponding systems are compared, those results obtained in this paper are confirmed by numerical simulation.
Keywords: pest-predator models, infinite delay, impulse, extinction, permanence
MSC numbers: 34K45, 34C25, 92D25
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