一类时间周期的时滞竞争系统行波解的存在性  

Existence of Periodic Traveling Waves for Time⁃Periodic Lotka⁃Volterra Competition Systems With Delay

作　　者：谷雨萌 黄明迪 GU Yumeng;HUANG Mingdi(School of Mathematics and Statistics,Xidian University,Xi’an 710071,P.R.China)

机构地区：[1]西安电子科技大学数学与统计学院,西安710071

出　　处：《应用数学和力学》2020年第6期658-668,共11页Applied Mathematics and Mechanics

基　　金：陕西省杰出青年科学基金(2020JC⁃24)。

摘　　要：该文研究了一类时间周期的时滞Lotka⁃Volterra竞争系统的行波解.首先,通过构造适当的上、下解,结合单调迭代的方法证明了当c<c∗时,存在连接两个半正周期平衡点的行波解,并且利用比较原理得到了周期行波解关于z的单调性.其次,通过单调性证明了行波解在正、负无穷远处的渐近行为.最后,证明了当c=c∗时周期行波解的存在性.A time⁃periodic reaction⁃diffusion Lotka⁃Volterra competition model with delay was considered.Under certain conditions,with the method of super⁃and sub⁃solutions and mono⁃tone iterations,the existence of time⁃periodic traveling waves connecting 2 semi⁃trivial periodic solutions of the corresponding kinetic system was proved with wave speed c<c∗.Further⁃more,the traveling wave solutions for c<c∗were proved to be monotone with the comparison principle,and the asymptotic behaviors of traveling wave solutions were obtained at minus/plus infinity.Finally,the existence of traveling wave solutions was proved at wave speed c=c∗.

关 键 词：扩散竞争系统 时滞模型 周期行波解 渐近行为 

分 类 号：O175.14[理学—数学]