JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (8): 73-81.doi: 10.6040/j.issn.1671-9352.0.2021.782

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Steady-state solutions of a Holling type Ⅱ competition model in heterogeneous environment

Zipeng HE(),Yaying DONG*()   

  1. School of Science, Xi’an Polytechnic University, Xi’an 710048, Shaanxi, China
  • Received:2021-12-02 Online:2023-08-20 Published:2023-07-28
  • Contact: Yaying DONG E-mail:1007044505@qq.com;dongyaying@xpu.edu.cn

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Abstract:

The steady-state solutions of a competitive model with Holling type Ⅱ functional response function in heterogeneous environment is investigated. Using the spectral theory of linear operators and comparison principle of parabolic equations, the global asymptotic stability of the trivial and semi-trivial solutions of the model is obtained, and the sufficient conditions for the competitive repulsion of two species are derived. With the help of topological degree theory, the sufficient conditions for the existence of positive steady-state solutions are established, which gives the sufficient conditions for the coexistence of the two species.

Key words: competitive model, Holling typeⅡ, heterogeneous environment, stability, degree theory

CLC Number: 

  • O175.26
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