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

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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.

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Authors and Affiliations

  1. School of Mathematics Science, University of Electronic Science and Technology of China, Chengdu, 610054, P.R. China

    Zijian Liu, Shouming Zhong & Chun Yin

  2. Key Laboratory for NeuroInformation of Ministry of Education, University of Electronic Science and Technology of China, Chengdu, 610054, P.R. China

    Shouming Zhong

  3. School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu, 610054, P.R. China

    Wufan Chen

Authors
  1. Zijian Liu
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  2. Shouming Zhong
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  3. Chun Yin
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  4. Wufan Chen
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Corresponding author

Correspondence to Zijian Liu.

Additional information

This research was supported by National Basic Research Program of China (2010CB732501) and the National Natural Science Foundation of China (NSFC No. 60873102 and 30970305).

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Liu, Z., Zhong, S., Yin, C. et al. On the Dynamics of an Impulsive Reaction-Diffusion Predator-Prey System with Ratio-Dependent Functional Response. Acta Appl Math 115, 329–349 (2011). https://doi.org/10.1007/s10440-011-9624-8

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  • DOI: https://doi.org/10.1007/s10440-011-9624-8

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