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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2021, Vol. 38 ›› Issue (5): 679-690.doi: 10.3969/j.issn.1005-3085.2021.05.007

• • 上一篇    下一篇

一类比率型 Holling-Leslie 趋化模型的分支结构

张  望,   李艳玲,   周  浩   

  1. 陕西师范大学数学与信息科学学院，西安 710119
  • 出版日期:2021-10-15 发布日期:2021-12-15
  • 通讯作者: 李艳玲 E-mail: yanlingl@snnu.edu.cn
  • 基金资助:
    国家自然科学基金 (61672021).

Bifurcation Structures for a Class of Ratio-type Holling-Leslie Chemotaxis Models

ZHANG Wang,   LI Yanling,   ZHOU Hao   

  1. School of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710119
  • Online:2021-10-15 Published:2021-12-15
  • Contact: Y. Li. E-mail address: yanlingl@snnu.edu.cn
  • Supported by:
    The National Natural Science Foundation of China (61672021).

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摘要：

本文研究了一类比率依赖型 Holling-Leslie 捕食-食饵的趋化模型，利用线性化方法和局部分支方法，以趋化敏感性系数 $\chi$ 为分支参数，在二维空间区域详细讨论非常数正平衡解的结构以及在分支点附近确定了分支方向．理论结果表明了趋化排斥具有不稳定性作用，能够导致局部分支解的产生．最后通过数值模拟验证了理论预测的正确性，解释了在趋化因子的作用下，生化系统会从均匀稳定态变成不稳定的生物现象．

关键词: 趋化, 平衡解, 渐近稳定, 局部分支

Abstract:

In this paper, a kind of rate-dependent Holling-Leslie predator-prey chemotaxis model is studied by using linearization method and local bifurcation theory. We discuss the structure of the normal positive equilibrium point in detail in two dimensional space with the prey-tactic sensitivity coefficient as bifurcation parameter and the bifurcation direction is determined near the bifurcation point. The theoretical results show that chemotactic rejection has an unstable effect and can lead to local bifurcation solutions. Finally, the theoretical prediction is verified by numerical simulation, and it is explained that the biochemical system would change from a homogeneous stable state to an unstable biological phenomenon.

Key words: chemotaxis, equilibrium solution, asymptotically stable, local branch

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