Modeling And Analysing The Population Ecology Of Empoasca Onukii Matsuda With Tea-leaves

As we know,how to make full use of mathematical models to solve practical problems by using of differential equations is a very important topic in applied mathematics,which has profound theoreti-cal value and application value.In this paper,we choose the dynamics of tea-leaves and Empoasca onukii Matsuda as the subject.After a long period of research and improvement,it is the first time to use differential equations to model the dynamical behavior of tea-leaves and Empoasca onukii Matsuda and analyze the dynamical behavior of the model.The model built in this paper has important originality and practical significance,and has a profound application prospect in the tea production.The main work of this paper is divided into three parts:first-ly,after understanding the background knowledge of Longjing tea-leaves and three stages of Empoasca onukii Matsuda(eggs,nymphs and adults),we take into account the growth rate,mortality and pick-ing rate of tea-leaves,the total number and the development rate of Empoasca onukii Matsuda,etc.,then a new four-dimensional stage-structured model is built.The positive invariance,boundedness,the local stability and global stability of its boundary equilibrium and positive equilibrium are investigated.The results are also verified by numerical simulations.Thirdly,we improve the model to make the model more useful in practical tea plantation.Actually,Empoasca onukii Matsuda in three stages has different damage rates to different parts of tea-leaves,and mainly injure the tender parts,also,adults do harm to older leaves.We divide tea-leaves into two stages:tender shoots and old leaves,all the old leaves are transformed from tender shoots.Empoasca onukii Matsuda has three stages,and different stages have different damage rates.In view of the above factors and more practical factors,a five-dimensional complex dynamical system model is originally built in this paper.