| Water eutrophication has a great impact on the ecological environment and the growth of aquatic products.After water eutrophication,it is easy to cause a single species of wild growth,outbreaks of water bloom,and even have a serious impact on human production and life.In order to control this phenomenon,Many measures can be taken,such as physical methods,biological methods and chemical methods,etc.In this paper,the relationship between excessive nutrients and phytoplankton growth after eutrophication of water body is considered,and the control mode implemented by human is characterized by pulse and switching.In this paper,ordinary differential equation,impulse differential equation and state switching equation are used to study and solve the bloom problem.This paper is divided into four parts:In the first chapter,the paper introduces the background of water environment,the measures to control water bloom,the research status of mathematical model and the preliminary knowledge.In chapter 2,on the basis of relevant model,the mathematical model of the interaction between nutrients,producers(phytoplankton,etc.)and consumers(zooplankton,etc.)and the mini model of nutrient-phytoplankton are established.The positive,boundedness,existence and stability of equilibrium and saddle-node bifurcation of the model are analyzed,and the corresponding numerical simulation is given.These results show that the system has complex dynamic properties,which correspond to phytoplankton Extinction,stability and multiple equilibrium states.The existence of two equilibrium states indicates that the phytoplankton growth results are related to the initial value.Different initial values will make the system approach to different equilibrium states.In chapter 3,On the basis of the second chapter,the semi-continuous dynamical system model of nutrient-phytoplankton mini model is established The mathematical results show that the phytoplankton can be controlled within an appropriate range or by using the state pulse control method In this way,the bloom can be controlled.In chapter 4,Filippov was established for algae growth in eutrophic water System model,qualitative analysis of state switching model subsystem,and sliding mode area and sliding mode dynamics and Filippov The sliding branches of the system are analyzed,and the numerical simulation of the state switching model is given.The mathematical results show that different control thresholds of h determine the stability of the system in different states,that is,the floating When plants set different density thresholds,the growth state of phytoplankton will tend to different equilibrium state. |
