一维格上时滞微分系统的行波解  

Traveling Waves of a Delayed Differential System in a Lattice

作　　者：曹华荣 吴事良 CAO Huarong;WU Shiliang(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》2018年第5期592-610,共19页Applied Mathematics and Mechanics

基　　金：中央高校基本科研业务费(JB160714)

摘　　要：针对部分种群个体活动而其他个体静止的单种群模型,主要研究了一维格上具有静止阶段的时滞反应扩散系统的行波解的定性性质.在单稳和拟单调的假设条件下,首先,研究了行波解的存在性.其次,证明了行波解的渐近行为、单调性以及唯一性.最后,证明了所有非临界波前解(即波速大于最小波速的波前解)是指数渐近稳定的.The qualitative properties of traveling waves of a delayed differential system in a lat- tice with a quiescent stage were addressed. Under monostable and quasi-monotone assump- tions, the existence of the traveling wave solutions were first established. Then, the asymptotic behavior, monotonicity and uniqueness of all wave profiles were proved. The exponential as- ymptotic stability of all non-critical traveling fronts was finally oroved.

关 键 词：行波解 格微分系统 静止阶段 时滞 

分 类 号：O175.14[理学—数学]