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The Coexistence States of a Predator-Prey Model with Nonmonotonic Functional Response and Diffusion

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Abstract

In this paper, a predator-prey model with nonmonotonic functional response is concerned. Using spectrum analysis and bifurcation theory, the bifurcating solution and its stability of the model are investigated. We discuss the bifurcation solution which emanates from the semi-trivial solution by taking the death rate as a bifurcation parameter. Furthermore, by fixed point’s index theory, the result of existence or nonexistence of positive steady states of the model is also obtained.

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Authors and Affiliations

  1. College of Mathematics and Information Science, Shaanxi Normal University, Xi’an, Shaanxi, 710062, China

    Yunfeng Jia, Jianhua Wu & Hua Nie

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  1. Yunfeng Jia
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  2. Jianhua Wu
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  3. Hua Nie
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Correspondence to Yunfeng Jia.

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Supported by the National Science Foundation of China (10571115).

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Jia, Y., Wu, J. & Nie, H. The Coexistence States of a Predator-Prey Model with Nonmonotonic Functional Response and Diffusion. Acta Appl Math 108, 413–428 (2009). https://doi.org/10.1007/s10440-008-9319-y

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  • DOI: https://doi.org/10.1007/s10440-008-9319-y

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