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Permanence and periodic solutions for an impulsive reaction-diffusion food-chain system with Holling type III functional response. (English) Zbl 1210.35278
Summary: An impulsive reaction-diffusion periodic food-chain system with Holling type III functional response is presented and studied in this paper. Sufficient conditions for the ultimate boundedness and permanence of the food-chain system are established based on the upper and lower solution method and comparison theory of differential equation. By constructing appropriate auxiliary function, the conditions for the existence of a unique globally stable positive periodic solution are also obtained. Some numerical examples are shown to illustrate our results. A discussion is given in the end of the paper.
MSC:
35R12Impulsive partial differential equations
35Q92PDEs in connection with biology and other natural sciences
92D25Population dynamics (general)
35A15Variational methods (PDE)
35B09Positive solutions of PDE
35B10Periodic solutions of PDE
35B35Stability of solutions of PDE
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