| Compared with conventional di?erential equation, impulsive di?erential equa-tion can describes the instantaneous change or jump of some states of motion at thecertain time, and it is more accurate to depict life phenomena and human exploita-tion on biologic resource in the real world. Impulsive di?erential equation playsan very important role in describing population dynamic behaviors. Based on theexploitation and utilization strategies of biological resources, the population biologymodels with time delay and impulsive are considered in this paper.Firstly, a delayed predator-prey model with continuous harvesting predator andimpulsive stocking prey is researched. Applying the comparison theorem of impul-sive di?erential equation, we obtain the su?cient conditions of the global attractivityof predator-extinction periodic solution and the permanence of the system. UsingMatlab, numerical simulations confirm the theoretic results obtined.Secondly, a delayed predator-prey model with impulsive harvesting predatorand stocking prey is discussed. Harvesting predator and stocking prey are finished inthe same time. By using comparison theorem, the su?cient conditions of the globalattractivity of the mature prey-extinction periodic solution and the permanence ofthe system are obtained. Numerical simulations verify our analytic results.Finally, a delayed predator-prey model with harvesting predator and stockingprey in di?erent time is considered. Using the comparison theorem, we obtain thesu?cient conditions of the global attractivity of the mature prey-extinction periodicsolution and the permanence of the system. Numerical simulations are inserted toillustrate the feasibility of our theoretical results. |
