Variable Consumption Plankton Model Under Two Nutritional Conditions

Sustainable development of aquaculture depends not only on aquaculture and fishing technology,but also on the environment of aquatic ecosystem.The health of water quality is the key factor affeeting the healthy development of aquaculture.In water environment,lack or excess of nutrients can lead to poor nutrition or eutrophication in healthy water body.Poverty and eutrophication of water body will greatly hinder the development of aquatic industry.Artificial management measures are needed to improve water quality.Based on the problem of aquaculture management,the concept of variable consumption is introduced in this paper.The interaction between nutrition and plankton is investigated by using impulse differential equation and ordinary differential equation,and the related mathematical problems is studied.The first chapter introduces the present situation of aquaculture,water environment and the artificial management measures for different water bodies.The research status of relevant biomathematical models and some preliminary knowledge are also introduced.In the second chapter,the nutrient consumption rate of plankton is regarded as a function of nutrient concentration,and a nutrient-plankton model with variable consumption rate is established.The positive and boundedness of solutions for continuous system are analyzed,the existence and stability of positive equilibrium are discussed.By discussing the existence of limit cycles,it is shown that the number of plankton varies periodically under certain conditions.In the third chapter,based on the aquaculture situation and the management measures of poor nutrient water,considering the effect of periodic nutrient input on water body on the basis of chapter 2 model,a kind of plankton model with periodic nutrient input is established.The conditions for the existence and global stability of periodic solution to phytoplankton extinction are studied.In the fourth chapter,aiming at the idea of algae removal by coagulation sedimentation in eutrophic water,a nutrient-phytoplankton model with state pulse control is established on the basis of chapter 2 model,considering the state feedback control of phytoplankton.The existence and stability of order-1 periodic solution are discussed by means of successor fuction and Poincaré map.