Dynamic Analysis Of Mathematical Models In Three Types Of Water Ecosystems

Phytoplankton,as the basis of aquatic food chain,plays a key role in primary production,nutrient cycle and food web.In the production and life of industry and agriculture,more and more organic wastes are discharged into the water body,resulting in excessive accumulation of nitrogen,phosphorus and other nutrients in the water body,which makes the eutrophication of the water body and the water pollution caused by it more and more prominent.Therefore,the research on plankton population and related biological treatment is particularly important.This dissertation mainly establishes different dynamic models for the allelopathy of phytoplankton and the interaction of nutrients,phytoplankton and zooplankton,and considers the effectiveness of some control measures.This dissertation is divided into four parts.In the first chapter,the problem of phytoplankton explosion caused by water eutrophication and some control measures are introduced.The research status of corresponding mathematical models and the related basic knowledge used in this dissertation are introduced.In the second chapter,according to the design idea of the turbidostat with feedback control of dilution rate in the laboratory,considering the control of ecological water regulation on cyanobacteria bloom,the variable structure model is introduced to describe this process,and a class of Filippov dynamics model of nutrition phytoplankton is constructed.Using Filippov convex method,the sliding mode dynamics of Filippov system is studied.Finally,the conclusion is numerically simulated and the biological significance is given.In the third chapter,considering that the nutrient of phytoplankton after death returns to the water body and then add the concentration of nutrients in the water body,the phytoplankton population size is set within a controllable economic threshold range by considering the characteristics of the material cycle and the ecosystem.A nutrition phytoplankton model with two-state dependent impulse control is established,and the qualitative properties of the continuous system are studied.And the sufficient conditions for the existence of order-1 and order-2 periodic solutions of impulsive systems under certain conditions.The stability of order-1 and order-2periodic solutions is demonstrated by the category Poincar?e criterion.In the fourth chapter,this chapter discusses the study of fractional-order models of toxic-phytoplankton-zooplankton systems to improve the stability of the system by designing generalized controllers,theoretically demonstrating that controlling periodic phytoplankton outbreaks is feasible.