外来入侵生物阶段结构模型的稳定性

A Class of Stage Structure Model of Alien Invasive Organisms

摘要: 该文研究外来生物入侵植物问题，考虑携带有害生物和患病两个阶段的植物树种，建立了一类生物入侵的植物病虫害模型，给出了其无病平衡点和正平衡点，通过建立适当的Lyapunov泛函，利用LaSalle不变集原理和Liapunov稳定性理论证明了无病平衡点的全局稳定性，通过稳定性理论的分析，得到正平衡点渐近稳定的充分条件。

Abstract: This paper studies the problem of alien organisms invading plants, considers plant species that carry pests and disease stages, establishes a model of biological invasive plant diseases and pests, and presents its disease-free balance point and positive balance point. By establishing proper Lyapunov functionals, the LaSalle invariant set theory and Liapunov stability theory are used to prove the global stability of the disease-free equilibrium. Through analysis of stability theory, a sufficient condition for the asymptotic stability of the positive equilibrium is obtained.