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Permanence and periodic solutions for an impulsive reaction-diffusion food-chain system with holling type III functional response |
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| Authors: | Zijian Liu Shouming Zhong Xiaoyun Liu |
| Affiliation: | a School of Mathematics Science, University of Electronic Science and Technology of China, Chengdu 610054, PR China b Key Laboratory for NeuroInformation of Ministry of Education, University of Electronic Science and Technology of China, Chengdu 610054, PR China c School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu 610054, PR China |
| Abstract: | 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. |
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