一类比率型Holling-Leslie趋化模型的分支结构  

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

作　　者：张望 李艳玲[1] 周浩 ZHANG Wang;LI Yanling;ZHOU Hao(School of Mathematics and Information Science,Shaanxi Normal University,Xi'an 710119)

机构地区：[1]陕西师范大学数学与信息科学学院,西安710119

出　　处：《工程数学学报》2021年第5期679-690,共12页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(61672021).

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χ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.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.

关 键 词：趋化 平衡解 渐近稳定 局部分支 

分 类 号：O175.26[理学—数学]