Quantitative Description And Qualitative Analysis Of Invasive Alien Plants

In recent years,alien invasive plants have attracted extensive attention from experts and scholars as well as from the public.It is not only a scientific issue,but is gradually becoming a globally shared ecological problem.Therefore,studying the diffusion law of invasive plants can grasp their invasive conditions and proliferation trends,which is of great significance for the development of reasonable control measures.This article will use this as a background to establish a dynamic model of the spread of alien invasive plants,study the law of the spread of invasive alien plants,provide theoretical basis and recommendations for the relevant state departments to formulate measures.To study the diffusion model of invasive alien plants with forest-age structure.First,we prove the existence of non-invasive equilibrium and positive-equilibrium points,and give the basic reproductive number;then we prove the local asymptotic stability of the non-invasive equilibrium and positive-equilibrium points;finally,the equilibrium is proved by the Lyapunov-LaSalle invariant set principle.The persistence points and the global asymptotic stability of the non-invasive equilibrium and positive-equilibrium points are proved by Lyapunov functions.The two-group structure model of invasive plants with growth function was studied.The existence of non-invasive equilibrium point and positive-equilibrium point of the model was obtained.The local asymptotic stability condition of the equilibrium point was given,that is,when the growth function reached a certain value and when₀R?27?1,then The system always has a locally asymptotically stable non-invasive equilibrium point;And when₀R?29?1,at that time,the non-invasive equilibrium point was unstable,and there was a positive equilibrium point that was locally asymptotically stable.Finally,numerical simulations verify the asymptotic stability of the positive equilibrium.