JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2015, Vol. 50 ›› Issue (03): 80-87.doi: 10.6040/j.issn.1671-9352.0.2014.339

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Dynamics research in a predator-prey system with a nonlinear growth rate

YANG Wen-bin, LI Yan-ling   

  1. College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062, Shaanxi, China
  • Received:2014-07-21 Revised:2014-11-10 Online:2015-03-20 Published:2015-03-13

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Abstract: The paper is concerned with a predator-prey diffusive dynamics subject to homogeneous Dirichlet boundary conditions, where the predator population reproduces by the nonlinear function 1/(1+ev). Existence and uniqueness of coexistence states for the predator-prey system are investigated. Moreover, some asymptotic behaviors of time-dependent solutions are shown and some numerical simulations are done to complement the analytical results. The main tools used here include the implicit function theorem, the bifurcation theory and the perturbation technique.

Key words: reaction-diffusion equations, uniqueness, numerical simulation, stability, positive solution

CLC Number: 

  • O175.26
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