脉冲时滞Lotka-Volterra食物链系统的正周期解

利用一些分析技巧和重合度理论,得到一类具有脉冲和时滞Lotka-Volterra食物链系统存在正周期解的新结果.所得的结论表明:脉冲是对该食物链系统正周期解存在性是有影响的.特别地,在每个种群的内禀增长率(出生率a1和死亡率a2,a3)、种群间相互作用率(捕食率b1,2,b2,3和消化率b2,1,b3,2),以及非线性种内干扰反应系数αi,j都确定的情况下,可以通过适当控制每个种群的(投放率或收回率)hi,k,使每个种群达到平衡(即存在正周期解).

Positive Periodic Solutions of a Lotka-Volterra Food-Chain System with Impulses and Delays

By means of coincidence degree theory and some analysis techniques,we obtain a new result on the existence of positive periodic solutions to a Lotka-Volterra food-chain system with impulses and delays.The result showed that impulses have effects on the existence of positive periodic solutions of a Lotka-Volterra food-chain system.Especially,ifthe growth rate(the birthrate a1and the mortality a2,a2),the population interacting rate(the pery rate b1,2,b2,3 and digest rate b2,1,b3,2),and the nonlinear interference reaction coefficient(αi,j)of every one of populations are given,each population may be balanced by controlling the putting rate or recovering rate(hi,k)of every group.