A Class Of Blue-green Algae Are Controlled By Pulse Governance Model Research

According to cyanophyte’s biological change law and differential equation basic theory, the thesis establishes and analyzes the ordinary differential equation model of the cyanophytes and chub’s concentration change, the control cyanophytes models with a fixed time and state-dependent impulses. There have a significant theoretical and practical sense to studying these model.Firstly, for the ordinary differential equation model of the cyanophytes and chub’s concentration change, the stability of the equilibria and the existence and uniqueness of limit cycles are obtained by applying differential equation’s stability and the qualitative theory. Secondly, by Floquet and compar-ison theorem of impulsive differential equation, the sufficient conditions of the locally asymptotic sta-bility of cyanophytes extinction periodic solutions and the permanence of the system are obtained. At last, we mainly study the dynamic behaviors of control of cyanophytes systems with state dependent impulsive effects, when the amount of cyanophytes reaches the thresholdh,we can ues the methods of throwing in crucian craps and artificial removing cyanophytes to control the cyanobacterial boolm,by using the Poincare map,sufficent conditions for the existence and stability of semi-trivial solution and positive periodic solution are obtained.