中文摘要：

研究一类格上时滞单种群模型行波解的渐近行为.许多学者结合上下解及单调迭代的方法研究了该系统行波解的存在性,并且,所构造的上下解保证非临界行波解（波速大于临界波速c＊）具有指数渐近行为.本文借助于Ikehara定理的渐近理论不仅给出了该模型所有非临界行波解的指数渐近衰减行为,而且进一步得到了临界行波解（波速等于c＊,即临界波速）具有代数指数渐近衰减行为,完善并改进了这类行波解的渐近性结果.

英文摘要：

The asymptotic behaviors of traveling waves for a single species model with delays on lattices were investigated.The existence of traveling wave solutions of the system was studied by using the monotone iterative technique with the help of the upper and lower solutions,whose constructed structures can ensure the exponential asymptotic behaviors of non-critical traveling wave solutions （the wave speed is greater than the critical speed）.In the light of the asymptotic theory in the Ikehara theorem the exponential asymptotic behaviors of all non-critical traveling wave solutions were obtained and the algebraic exponential asymptotic behaviors of the critical traveling wave solutions （the wave velocity is equal to the critical velocity）were achieved.The results make up and improve the result on asymptotic behaviors of traveling wave solutions.