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《山东大学学报(理学版)》 ›› 2026, Vol. 61 ›› Issue (7): 93-107.doi: 10.6040/j.issn.1671-9352.0.2024.412

• 生物数学 • 上一篇    

一类非局部Field-Road模型的渐近传播速度

安达,张晓*   

  1. 西安电子科技大学数学与统计学院, 陕西 西安 710071
  • 发布日期:2026-07-01
  • 通讯作者: 张晓(1995— ),女,博士研究生,研究方向为微分方程、动力系统及其生物中的应用. E-mail:orso568390@163.com
  • 作者简介:安达(2000— ),男,硕士研究生,研究方向为微分方程、动力系统及其在生物中的应用. E-mail:2948553392@qq.com*通信作者:张晓(1995— ),女,博士研究生,研究方向为微分方程、动力系统及其生物中的应用. E-mail:orso568390@163.com

Spreading speed of a class of Field-Road models with nonlocal dispersal

AN Da, ZHANG Xiao*   

  1. School of Mathematics and Statistics, Xidian University, Xian, 710071, Shaanxi, China
  • Published:2026-07-01

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摘要： 针对传统局部扩散模型在刻画长距离传播上的局限性,本文基于Berestycki等提出的具有局部扩散的Field-Road模型,研究一类具有非局部扩散的Field-Road模型。首先,建立快速扩散路径加快物种传播速度的阈值并通过构造适当的上下解结合比较原理证明沿路方向上的渐近传播速度的存在性;其次,研究物种在路上的扩散速率、非局部扩散核函数的支集半径以及对流强度对渐近传播速度的影响。结果表明,3个参数均会加快渐近传播速度且其与扩散速率的平方根、支集半径以及对流强度保持同阶线性增长。

关键词: 场路模型, 渐近传播速度, 非局部扩散

Abstract: To address the limitations of traditional local dispersal models in characterizing long-distance propagation, this paper studies a class of Field-Road models with nonlocal dispersal, building on the Field-Road model with local dispersal proposed by Berestycki et al. Firstly, we establish the threshold of fast diffusion roads to accelerate spreading speed of species and prove the existence of spreading speed along the road direction by constructing appropriate super-and sub-solutions and combining the comparison principle. Secondly, the influences of the diffusion rate of species on the road, the support radius of the nonlocal dispersal kernel function and the convection intensity on spreading speed are studied. The results show that the three parameters all accelerate spreading speed and it maintains the same order linear growth with the square root of the diffusion rate, the support radius and the convection intensity.

Key words: Field-Road model, spreading speed, nonlocal dispersal

中图分类号: 

  • O175
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