一类扩散的捕食者-食饵模型行波解的存在性  

Existence of traveling wave solutions for a diffusive predator-prey model

作　　者：张行 焦玉娟[1] 杨进苗 Hang ZHANG;Yujuan JIAO;Jinmiao YANG(College of Mathematics and Computer Science,Northwest Minzu University,Lanzhou 730030,Gansu,China)

机构地区：[1]西北民族大学数学与计算机科学学院,甘肃兰州730030

出　　处：《山东大学学报（理学版）》2023年第10期97-105,共9页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(11761063);中央高校基本科研业务经费(31920220041)。

摘　　要：讨论一类扩散捕食者-食饵模型行波解的存在性。首先,通过线性化理论证明当c<c*时,该模型不存在行波解;其次,用上下解方法和Schauder不动点定理证明当c≥c*时,该模型存在弱行波解;再次,通过利用Lyapunov函数和Lasalle不变集原理证明在适当的条件下,该模型的弱行波解就是强行波解;最后,通过数值模拟来支撑已获得的理论结果的有效性。In this paper,we discuss the existence of traveling wave solutions for a diffusive predator-prey model.Firstly,using linearization method,we prove non-existence of traveling wave solutions for the model with c<c*.Secondly,we establish the existence of weak traveling wave solutions with c≥c*by applying upper and lower solution method and Schauder's fixed point theorem.Moreover,utilizing Lyapunov function and LaSalle's invariance principle,we obtain that the weak traveling wave solutions for the model are traveling wave solutions under the suitable conditions.Finally,the numerical experiments support the validity of our theoretical results.

关 键 词：行波解 捕食者-食饵模型 上下解 SCHAUDER不动点定理 LYAPUNOV函数 

分 类 号：O175.26[理学—数学]