一类密度依赖的生物入侵模型的周期行波解  

Period Travelling Wave Solutions of a Density-Dependent Biological Invasion Model

作　　者：刘园园 王勤龙 黄文韬 LIU Yuan-yuan;WANG Qin-long;HUANG Wen-tao(Guangdong University of Science and Technology,Dongguan 523668,China;School of Mathematics and Computational Science,Guilin University of Electronic Technology,Guilin 541004,China;College of Mathematics and Statistics,Guangxi Normal University,Guilin 541004,China)

机构地区：[1]广东科技学院基础部,广东东莞523668 [2]桂林电子科技大学数学与计算科学学院,广西桂林541004 [3]广西师范大学数学与统计学院,广西桂林541004

出　　处：《安徽师范大学学报（自然科学版）》2021年第3期227-232,共6页Journal of Anhui Normal University(Natural Science)

基　　金：国家自然科学基金项目(12061016);广西自然科学基金重点项目(2020GXNSFAA159138).

摘　　要：研究了一类密度依赖迁移和具有Allee效应种群动态的单种群反应扩散型的非线性偏微分方程,通过行波变换将其转化为行波方程,利用计算机代数系统Mathematica计算得到其一个正平衡点处的前几个焦点量,由此研究其Hopf分支得到了两个极限环,从而进一步获得两个特殊的周期行波解,即孤立波解,它对应于生物入侵种群的传播模式研究,有一定的实际意义。In this paper,a class of biological invasion model with density dependence on migration and Allee effect,which consists of a non-linear partial differential equation of advection-diffussion-reaction type is studied.The equation is transformed into the travelling wave equation by travelling wave transformation,and through the computer algebra Mathematica the first several focus values can be obtained.By investigating its Hopf bifcurction,two limit cycles were obtained,and two special periodic travelling wave solutions were obtained.It corresponds to the specific real propagation pattern in the biological invasion process,which is a meaningful discovery.

关 键 词：生物入侵 非线性模型 多重Hopf分支 行波解 

分 类 号：O175.12[理学—数学]