扩散捕食-食饵系统的周期行波解（英文）  

Periodic Travelling Wave Solution in a Diffusive Predator-prey System

作　　者：宋永利[1] 徐周[2] 

机构地区：[1]杭州师范大学理学院,浙江杭州310036 [2]同济大学数学系,上海200092

出　　处：《杭州师范大学学报（自然科学版）》2017年第4期368-377,共10页Journal of Hangzhou Normal University(Natural Science Edition)

基　　金：Supported by the National Natural Science Foundation of China(11571257);the Scientific Research Start-up Foundation of Hangzhou Normal University(201603)

摘　　要：研究一般的扩散捕食-食饵系统中周期行波解的存在性.首先,给出了波方程组中Hopf分支发生的条件;然后,以扩散系数为分支参数,推导出了周期行波解发生的临界值;最后,应用所得的理论结果研究了一个具有群体效应的捕食-食饵系统,获得了周期行波解存在的条件,并利用数值模拟例证了所得的理论结果.In this paper,the existence of the periodic travelling wave solution for a general diffusive predatorprey system is investigated.The condition for the occurrence of Hopf bifurcation in wave equations is provided firstly.Then,taking the diffusion coefficient as the bifurcation parameter,the critical value for the occurrence of periodic travelling wave solution is derived.Finally,the obtained theoretical results are applied to deal with a diffusive predator-prey system with herd behavior and the conditions for the occurrence of the periodic travelling wave solution are obtained.The numerical simulations are also employed to illustrate the theoretical results.

关 键 词：捕食-食饵系统 周期行波解 HOPF分支 

分 类 号：O19[理学—数学] O29[理学—基础数学]