具有时滞的离散Lotka-Volterra合作系统波前解的非线性稳定性  

Nonlinear Stability of Traveling Wavefronts for a Discrete Cooperative Lotka-Volterra System With Delays

作　　者：闫瑞[1] 刘桂荣[2] 李晓翠 YAN Rui;LIU Guirong;LI Xiaocui(School of Applied Mathematics,Shanxi University of Finance and Economics,Taiyuan 030006,P.R.China;School of Mathematical Sciences,Shanxi University,Taiyuan 030006,P.R.China;College of Mathematics and Physics,Beijing University of Chemical Technology,Beijing 100029,P.R.China)

机构地区：[1]山西财经大学应用数学学院,太原030006 [2]山西大学数学科学学院,太原030006 [3]北京化工大学数理学院,北京100029

出　　处：《应用数学和力学》2023年第4期461-470,共10页Applied Mathematics and Mechanics

基　　金：国家自然科学基金项目(11971279;12101034)。

摘　　要：反应扩散模型的行波解的稳定性是一个很重要的研究课题.该文主要研究了一类具有时滞的离散Lotka-Volterra合作系统波前解的全局非线性稳定性.具体来讲,当初值在无穷远处指数衰减到有较大波速的波前解而在其他位置可以任意大时,运用L^(2)-加权能量方法、比较原理和挤压技术可以得到该系统的此类波前解是指数渐近稳定的,并解决了离散扩散算子及时滞共同作用下建立能量估计的问题.总之,将加权能量方法推广到带有时滞的离散系统中,丰富了相关的研究内容.The stability of traveling wave solutions of the reaction diffusion model is a very important research topic.The globally nonlinear stability of traveling wavefronts for a discrete cooperative Lotka-Volterra system with delays was studied.More precisely,for the initial perturbation decaying exponentially to the traveling wavefronts with a relatively large speed at infinity,but arbitrarily large speeds in other positions,by means of the L^(2)-weighted energy method,the comparison principle and the squeezing technique,such traveling wavefronts were obtained and proved to be of exponentially asymptotic stability.Moreover,the problem of establishing the energy estimates was solved under the actions of the discrete dispersal operator and the time delays.In short,the extension of the weighted energy method to discrete systems with delays,enriches the relative research.

关 键 词：反应扩散系统 时滞 波前解 稳定性 

分 类 号：O175.7[理学—数学]