研究脉冲竞争系统周期解新的单调迭代方法(英文)

A New Monotone Iteration Method for Finding Periodic Solutions of Impulsive Competition System

文章研究了一类正常细胞和癌细胞相互作用的竞争系统周期解的存在性.数学模型包括竞争型的Lotka-Volterra方程组与描述周期性化疗的脉冲条件.文章建立了一类新的单调迭代方法,该方法是构造性的,周期解可以由一个线性迭代过程得到,每一步迭代只需求解一个脉冲微分方程初值问题.文章获得了系统至少存在一个严格正的周期解的充分条件.

This paper is concerned with the existence problem of periodic solutions for a normal and tumor cells competition model with impulsive effects. The mathematical problem involves a coupled system of Lotka-Volterra together with periodically pulsed conditions. The approach to the problem is by the method of upper and lower solutions and its associated monotone iterations. This method is constructive and the periodic solutions can be computed from a linear iteration process in the same fashion as for impulsive differential equation initial value problem, a set of easily verifiable sufficient conditions are obtained for the existence of at least one strictly positive periodic solutions.