JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2025, Vol. 60 ›› Issue (4): 84-92.doi: 10.6040/j.issn.1671-9352.0.2023.323

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Coexistence solutions of a predator-prey model with Allee effect and density-dependent diffusion in the predator

MA Tiantian, LI Shanbing*   

  1. College of Mathematics and Statistics, Xidian University, Xian 710126, Shaanxi, China
  • Online:2025-04-20 Published:2025-04-08

Abstract: This paper is concerned with the coexistence solutions of a predator-prey model with Allee effect and density-dependent diffusion in the predator under homogeneous Dirichlet boundary conditions. Based on a priori estimate of coexistence solutions, the sufficient conditions for the existence of coexistence solutions are established by using the theory of fixed point index in positive cone. The results show that the density-dependent diffusion has a significant effect on the existence of coexistence solutions, and it is also find that the functional response function between the two species has an essential effect on the existence of coexistence solutions.

Key words: predator-prey model, Allee effect, density-dependent diffusion, coexistence solutions, the theory of fixed point index

CLC Number: 

  • O175
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