草履蚧综合治理模型动力学性态分析

Dynamic analysis of a Drosicha corpulenta integrated management model

草履蚧在我国大部分地区都有分布,通过吸食树液致使树势衰弱,甚至枝条枯死,影响产量。本文在对草履蚧及其天敌大红瓢虫之间相互关系分析的基础上,首先建立了一个具有避难所效应及额外食物来源的捕食-被捕食模型,分析了系统平衡态及极限环的存在性和稳定性。其次,从控制草履蚧蔓延角度出发,建立了一个具有状态反馈的草履蚧综合治理模型,利用后继函数的方法证明了系统阶-1周期解的存在性,并借助类似庞加莱准则给出了阶-1周期解轨道渐近稳定性条件。最后,利用MATLAB对文中所取得的主要结论进行了仿真验证。本文研究为草履蚧综合治理提供了新的思路和方法。

Drosicha corpulenta is distributed in most areas of our country.It causes tree weakness,even branches dying,and affects yield by sucking tree SAP.In this paper,a predator-prey model with shelter effect and additional food source is established based on the relationship analysis between the Drosicha corpulenta and the Rodolia rufopilosaMuls.The existence and stability of equilibria and the limit cycle are analyzed.Secondly,from the point of view of controlling the spread of the Drosicha corpulenta,an integrated management model based on state-feedback is established.The existence of the order-1 periodic solution of the system is proved by the method of successor function,and the asymptotic stability condition of the order-1 periodic solution is given by means of Analogue Poincar criterion.Finally,the main results are verified by MATLAB simulations.The research in this paper provides a new idea and method for integrated management of Drosicha corpulenta.