The Study Of Some Classes Of Eutrophication Governance Model About Water

In this paper, we mainly study the dynamics of some classes of eutrophication governancemodel with a fxed time pulse control and state impulse control.The article includes four chapters.The preface is in chapter1, we introduce the research background of this article, the maintask and some important preliminaries.In Chapter2, a class eutrophication governance model with a fxed time pulse was studied.We analyzed the persistence of system by using scaling law and constructing a V function, andgot the sufcient condition of coexistence of alga and fsh. And by using the Floquet multipliertheory of impulsive diferential equation, we analyzed local asymptotically stable of the borderperiodic solution of system. A numerical analysis is given to show the correctness of the mainresults.In Chapter3, existence of periodic solution of a class eutrophication governance model withstate impulse studied. We discussed existence of periodic solution of system by constructingtwo categories Poincar′e mapping, then obtained the sufcient condition of existence of plusorder1periodic solution of system, and the sufcient condition of existence of order2periodicsolution of system. In the end, numerical simulations are carried out to explain the mathematicalconclusions.In Chapter4, existence and uniqueness of periodic solution of a class eutrophication gover-nance model with stata impulse was studied. We construct two more systematic to form a closedsimply connected bounded domain, and obtained existence and uniqueness of order1periodicsolution by using Lambert W function. Numerical simulations were carried out to illustrate themain theoretical results.