Dynamic Analysis Of SI Model With A Class Of Non-smooth Pest Control Strategy

As we all know that it is one of the main reasons why the significant losses of crops havebeen led for the diseases and insect pests caused by pest， it has to be caused the attention forscholars in all fields. According to the above biological background， the related researchwith pest control strategy in this paper is as follows.In the first chapter， we introduce some definitions and preliminary knowledge aboutthis paper; The second chapter， on the basis of integrated pest management， we build atwo class of populations SI model by spraying insecticide and dropping infected insect pestpopulations on fixed time， and study the dynamic quality of this model in detail and give thethreshold conditions of the pest extinction and the continuous survival; The third chapter， itis on the basis of the second chapter， we improve the original SI model and take theeconomic threshold policy. Here， we focus on the susceptible insect populations as controlindex and establish a epidemic Filippov model. In the third chapter， we systematic study theepidemic dynamics properties of Filippov model， including the sliding mode domain andexistence of sliding region， regular equilibria， virtual equilibria， pseudoequilibrium andboundary equilibria as economic threhold (ET) varies are given. By constructing appropriateLyapunov functions and Dulac function respectively， we show the global asymptoticstability of real equilibria (or boundary equilibria) and pseudo equilibrium. Finally， wediscuss some branch of parameters about Filippov systems.In addition，our theoretical results are simulated by mathematical Matlab software，andit is further confirmed the correctness of the theoretical results in this paper.