JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2022, Vol. 57 ›› Issue (1): 50-55.doi: 10.6040/j.issn.1671-9352.0.2021.259

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Properties of the species invasion model with Allee effect

ZHANG Bei-bei, XU Yao, ZHOU You, LING Zhi*   

  1. School of Mathematics and Science, Yangzhou University, Yangzhou 225002, Jiangsu, China
  • Published:2021-12-21

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Abstract: Based on the reaction diffusion equation with free boundary, the mathematical model of species invasion with Allee effect is established, the dynamic process of the invasive species is described, and the existence and uniqueness of the global solution of the model are explored. Focusing on the nature of the long-term solution, the corresponding conditions of the spreading or vanishing of the invasive species in the new environment are obtained, we have proved the conclusion that the possibility the specie will be vanish due to the small initial survival area or poor self-spreading ability, and verified our analytical findings numerically with MATLAB software. These results provide a theoretical basis for the prevention and control of ecological protection and harmful species invasion.

Key words: species invasion, free boundary, Allee effect, reflection-diffusion equation, spreading and vanishing

CLC Number: 

  • O175.26
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