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Positive solutions of a diffusive Leslie–Gower predator–prey model with Bazykin functional response

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Abstract

In this paper, we consider a diffusive Leslie–Gower predator–prey model with Bazykin functional response and zero Dirichlet boundary condition. We show the existence, multiplicity and uniqueness of positive solutions when parameters are in different regions. Results are proved by using bifurcation theory, fixed point index theory, energy estimate and asymptotical behavior analysis.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Southwest University, Chongqing, 400715, People’s Republic of China

    Jun Zhou

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  1. Jun Zhou
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Correspondence to Jun Zhou.

Additional information

Partially supported by NSFC grant 11201380, the Fundamental Research Funds for the Central Universities grant XDJK2012B007, Doctor Fund of Southwest University grant SWU111021 and Educational Fund of Southwest University grant 2010JY053.

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Zhou, J. Positive solutions of a diffusive Leslie–Gower predator–prey model with Bazykin functional response. Z. Angew. Math. Phys. 65, 1–18 (2014). https://doi.org/10.1007/s00033-013-0315-3

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  • DOI: https://doi.org/10.1007/s00033-013-0315-3

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