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Zbl 1210.35278
Liu, Zijian; Zhong, Shouming; Liu, Xiaoyun
Permanence and periodic solutions for an impulsive reaction-diffusion food-chain system with Holling type III functional response. (English)
[J] J. Franklin Inst. 348, No. 2, 277-299 (2011). ISSN 0016-0032; ISSN 1879-2693/e

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 2000:: *35R12 Impulsive partial differential equations
35Q92
92D25 Population dynamics
35A15 Variational methods (PDE)
35B09
35B10 Periodic solutions of PDE
35B35 Stability of solutions of PDE

Keywords: impulsive reaction-diffusion system; food-chain system; stable positive periodic solutions

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