Abstract
基于生态学理论与数学生物学知识，在动态建模过程中加入了Hassell-Varley功能反应函数，建立了一类具有季节效应的脉冲控制生物动力系统。借助脉冲微分方程的Floquet定理与比较定理，分析了系统半平凡周期解的存在性、局部渐近稳定性和全局渐近稳定性，同时讨论了系统生物种群的灭绝性与持久生存性。这些研究结果为进一步研究如何运用脉冲控制策略维持生态种群持久生存提供了一定的理论支撑。 In this paper, firstly, on the basis of ecology theory and mathematical biology knowledge, an impulsive controlled biological dynamical system with seasonal effect has been established by introducing Hassell-Varley functional response in the process of dynamic modeling. Secondly, using the Floquet theory and comparison theorem of impulsive differential equations, the existence, local asymptotic stability and global asymptotic stability of the semi-trivial periodic solution have been analyzed, and then the extinction and permanence of biological populations in the system have also been discussed. Finally, all those results can provide some theoretical support for further researching how to utilize control strategy to maintain the survival of ecological populations.
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