On the Dynamics of an Impulsive Reaction-Diffusion Predator-Prey System with Ratio-Dependent Functional Response

Authors:
Zijian Liu;Shouming Zhong;Chun Yin;Wufan Chen
Affiliations:
School of Mathematics Science, University of Electronic Science and Technology of China, Chengdu, P.R. China 610054;School of Mathematics Science, University of Electronic Science and Technology of China, Chengdu, P.R. China 610054 and Key Laboratory for NeuroInformation of Ministry of Education, University of ...;School of Mathematics Science, University of Electronic Science and Technology of China, Chengdu, P.R. China 610054;School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu, P.R. China 610054
Venue:
Acta Applicandae Mathematicae: an international survey journal on applying mathematics and mathematical applications
Year:
2011

Citing 2
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Global stability of a reaction-diffusion predator-prey model with a nonlocal delay

Mathematical and Computer Modelling: An International Journal

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Abstract

An impulsive reaction-diffusion periodic predator-prey system with ratio-dependent functional response is investigated in the present paper. Sufficient conditions for the ultimate boundedness and permanence of the predator-prey 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 presented to verify our results. A discussion is given in the end of the paper.