Existence of Periodic Traveling Waves for Time-Periodic Lotka-Volterra Competition Systems With Delay
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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
*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. Abstract: 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 monotone 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*.Furthermore, the traveling wave solutions for 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*. -
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