JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2019, Vol. 54 ›› Issue (9): 54-61.doi: 10.6040/j.issn.1671-9352.0.2018.667

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Qualitative analysis of a diffusive predator-prey model with density dependence

LI Hai-xia   

  1. Institute of Mathematics and Information Science, Baoji University of Arts and Sciences, Baoji 721013, Shaanxi, China
  • Online:2019-09-20 Published:2019-07-30

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Abstract: The uniqueness of coexistence solutions and asymptotic behavior for a diffusive predator-prey model with density dependence are studied. The sufficient conditions of the existence of coexistence solutions are given by means of the fixed point index theory. Then, by making use of the perturbation theory for linear operators, we discuss the stability and uniqueness of coexistence solutions. Finally, the conditions of the extinction and permanence for the system by the comparison principle for parabolic equations, and the theoretical results of asymptotic behavior for the system are verified by some numerical simulations. The results show that the two species can coexist and the system has a unique coexistence solution under certain conditions.

Key words: a diffusive predator-prey model, density dependence, fixed point index, perturbation theory, uniqueness, asymptotic behaviour

CLC Number: 

  • O175.26
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