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

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.