Association Journal of CSIAM
Supervised by Ministry of Education of PRC
Sponsored by Xi'an Jiaotong University
ISSN 1005-3085  CN 61-1269/O1

Chinese Journal of Engineering Mathematics ›› 2024, Vol. 41 ›› Issue (4): 727-740.doi: 10.3969/j.issn.1005-3085.2024.04.009

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Spatial Patterns of a Predator-prey Model with Prey Refuge and Nonlocal Predation Effect

WANG Caiyun1,  LI Jing2,  YANG Ruilan1,  LAN Wangsen1   

  1. 1. Department of Mathematics, Xinzhou Teachers University, Xinzhou 034000
    2. School of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan 030006
  • Received:2023-05-04 Accepted:2024-03-07 Online:2024-08-15
  • Contact: J. Li. E-mail address: jingli_2016@126.com
  • Supported by:
    The National Natural Science Foundation of China (12001340; 11671241); the Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi Province (2019L0472).

Abstract:

Predator-prey reaction-diffusion model with refuge effect is an important type of population dynamics model, and its pattern formation provides key information for studying the spatiotemporal distribution of population. A Leslie-Gower predator-prey reaction-diffusion model with both refuge and nonlocal predation effects is proposed. Firstly, the conditions for local stability and Turing instability of the positive equilibrium point are derived through linear stability analysis and Turing instability analysis, respectively. Secondly, the evolution of the patterns of the prey with nonlocal predation and refuge effects was demonstrated through numerical simulations. Finally, by analyzing the relationship between the spatial mean density of predator and prey populations and the changes in nonlocal prey and refuge effect parameters, it is shown that the spatial mean density of prey increases, while the number of predator decreases with the enhancement of nonlocal predation effects, indicating that nonlocal effects promote the growth of prey density while inhibiting the growth of predator populations; The spatial mean density of predator and prey increases simultaneously with the enhancement of refuge effect, indicating that strong refuge effect has a protective effect on prey and can promote the persistence and coexistence of predator and prey. The result helps people better understand the law of nonlocal effects and refuge effects on the pattern formation of predator and prey from a mathematical perspective.

Key words: prey refuge, nonlocal predation effect, pattern, predator-prey model, reaction diffusion system

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