A Study On The Dynamics Of Ecological Model With Several Kinds Of Nutrient-Phytoplankton

Based on the nonlinear dynamics theory and knowledge of aquatic ecology,the paper constructs several aquatic ecological dynamical system.The specific dynamical behavior is studied and some relevant judgment criterion is received.Firstly,the introduction part briefly introduces the research background and research status of prediction and control of eutrophication in water bodies.In addition,some basic theorem and important lemmas,which are frequently used in the following chapters,are also presented.Secondly,the dynamical model of a nutrient-phytoplankton with a state impulsive control feedback is discussed.The Michaelis-Menten Functional response function is introduced for the purpose of portraying the interaction mechanism between the phytoplankton and nutrient.The sufficient criterion of the system about the existence,uniqueness and orbital asymptotic stability is also discussed.The result provides theoretical foundation for the entirely studying the theory of state impulsive feedback control in the appliance of eutrophication prevention.Once more,the dynamical model of a nutrient-predator with a state impulsive control feedback is discussed,and the nutrient cycling items are introduced to describe the influence mechanism of nutrient circulation in the aquatic ecosystem.The sufficient criterion of the system about semi-trivial periodic solution and the order-1 positive periodic solution are discussed.The study provides theoretical support for the system to clarify the influence mechanism of nutrient circulation in aquatic eutrophication.Finally,a nutrient-algal population growth dynamical model under a kind of total phosphorus is discussed.The distributed delay item is introduced for describing the time delay mechanism about algal population absorbing nutrient and translating it for growth nutrient substance.