Dynamics Of A Nutrient-phytoplankton Model With Impulisve State Feedback Control

In recent years,the environmental problems caused by phytoplankton bloom have seriously affected the economic development,and even posed a certain threat to human health,which makes the study of phytoplankton population growth control strategy more concerned.Therefore,based on the theories of population dynamics and impulsive dynamics,this paper constructs a class of nutrient-phytoplankton model with state impulsive feedback control,and studies the dynamics of phytoplankton population growth control.Firstly,the impulsive feedback control dynamical model based on the growth state of phytoplankton is constructed and analyzed theoretically and numerically.The existence and uniqueness and global asymptotic stability of the equilibrium for the reduced system without impulsive state feedback control are investigated.The existence of periodic solutions of the system with state impulsive control,especially the order-1 and order-2 periodic solution,is further studied by using successor function.And some sufficient conditions for the stability of the order-1 periodic solution are obtained.Secondly,based on the related research work in chapter 2,chapter 3,considering the impulse feedback control which depends on the state of nutrient concentration in water body,establishes the dynamic system with the impulse feedback control which depends on the state of nutrient concentration.Sufficient conditions for existence and the stability of semi-trivial periodic solution can be studied by the analogue of the Poincaré criterion.Moreover,the existence of the order-1 is discussed by using Poincaré mapping under certain conditions.Finally,based on the research work in Chapter 2,Chapter 4 considers asynchronous control of phytoplankton population growth.An early warning value is set up to limit the growth of phytoplankton by controlling nutrient concentrations when the density of phytoplankton reaches an early warning value;and to treat phytoplankton when the density of phytoplankton reached the critical value of outbreak.And the corresponding dynamic model was constructed.By using geometric methods and successor functions,the existence of the system order-1 periodic solution is proved,and it is obtained that the system has at least two order-1 periodic solutions under certain conditions.The results of numerical simulation also fully confirm the complex dynamic behavior of the system.