具有Leslie-Gower项捕食-食饵模型的同伦分析解法  

Homotopy Analysis Method to a Kind of Leslie-GowerPredator-prey Model

作　　者：李晓艳 LI Xiao-yan(School of Information Engineering,Lanzhou City University,Lanzhou Gansu 730070)

机构地区：[1]兰州城市学院信息工程学院,甘肃兰州730070

出　　处：《甘肃高师学报》2023年第5期14-17,共4页Journal of Gansu Normal Colleges

基　　金：2021年甘肃省高校课程思政示范项目“思政视角下《实变函数》课程的开发与研究”。

摘　　要：利用同伦分析方法,研究了具有Leslie-Gower功能反应函数的捕食-食饵模型.首先讨论了该模型解的不变集,得到系统的解为正解且有界;然后利用水平吹胀和垂直吹胀的方法得到了系统在原点的不稳定性;最后研究了该模型的低阶和高阶近似解析解.这一系列近似解可用于分析此模型解析解的性质,从而得到该模型两种群随时间变化的动力学行为.A predator-prey model with Leslie-Gower reaction function was studied by homotopy analysis method.Firstly,the invariant set of solutions of the model was discussed,and the solution of the system was positive and bounded.Then,the instability of the model at the origin was obtained by horizontal and vertical blowing-up methods.Finally,the lower order and higher order approximate analytical solutions of the model were obtained.The series approximate analytical solutions can be used to analyze the properties of the model,so as to obtain the dynamic behavior of the two populations with time.

关 键 词：Leslie-Gower捕食-食饵模型 同伦分析方法 近似解 

分 类 号：O175[理学—数学]