The Study On Control Of Cyanophytes Systems With Different Removal Rate

In this paper,we mainly investigate the categories with different removal rate of cyanophytes dynamics properties of controlling model, including ordinary differential system, a complex dy-namics system which has a fixed time pulse control and state pulse control. These systems convey important theoretical and realistic significance. This thesis includes four chapters:The first chapter is introduction, which mainly explains the research background, the main task of the thesis and some important preliminaries.The second chapter,we build a model which mainly discusses the method of controlling the growth of cyanophytes by the planting water hyacinth with violet root. This special root can release an inhibitor in the process of growth which can effectively inhibit the growth of cyanophytes. By using the method of analysis and the Routh Hurwitz criterion to discuss the existence and locally asymptotic stability of the two equilibrium point to illustrate whether the method of the control of cyanophytes will be successful; Then according to lyapunov function V(s(t),x1(t),x2(t)) by studying the properties of V function to investigate three stable equilib-rium state of the global asymptotic stability. At the final stage, digital simulation is carried out for the each stage which made the paper more complete and clear.The third chapter,we mainly discusses the a model which mainly discusses the method of controlling the growth of cyanophytes with fixed time pulse control, namely, on the basis of Spraying chemicals at a fixed time combining with planting the water hyacinth with violet root artificially, through which can effectively control the spreading of blue-green algae. Through analyzing the extinction the periodic solution of the algae and conditions that a system is able to living persistently, which can be effectively control the actual data. Accordingly, the growth of the algae madness can be better controlled so that the purpose of cyanobacterias’control achieved.The fourth chapter, we mainly discusses the a model which mainly discusses the method of controlling the growth of cyanophytes with state pulse control. By observing the growth of algae and the Number of cyanobacteria to determine whether spraying chemicals,on the basis of Spraying chemicals at a fixed time combining with planting the water hyacinth with violet root artificially when the number of cyanobacteria reaches a certain critical value. Using two methods to effectively control the growth of algae is better than one of them. In the thesis, the existence conditions of the boundary periodic solution and the positive periodic solutions is discussed and sufficient conditions for the orbit asymptotic stability of the periodic solutions are achieved...