Research On Controlling Model Of Three Classes Of Waters Ecosystem

Fishery production depends not only on fishery production technology,but also on aquatic ecological environment and its resources.Healthy water can promote the development of fisheries.It is necessary to study biological resources and human management measures to maintain water health.At present,many water bodies,due to eutrophication,cause algae to multiply in large numbers.Some of these algae even produce toxins,affecting fishery resources in water bodies,and then affect the fishery production.In this paper,the fishery problem is considered in the process of modeling.In view of different fishery production strategies,the relationship between nutrient phytoplankton and zooplankton is considered.The ordinary differential equation,impulsive differential equation,state switching equation and so on are used to describe and study the related problems.This paper is divided into four parts.The first part introduces fishery resources,water ecological environment,the background of fishery ecological environment,the present situation of mathematical research on fishery model,and the relevant basic knowledge to be used in this paper.In the second part,according to the situation of fishery production and the control of plankton resources,the effects of a class of periodic pulses on fish production are considered.Based on the population model,a class of fishery models with toxic effect and consumers are established.Through the theory of Floquet,the qualitative and stability studies are carried out,and some problems such as the threshold value of input are discussed.The existence and global stability of the periodic solution for algae extinction are obtained.In the third part,considering the effect of a class of state impulse feeding consumers(fish)on fishery production and management,a kind of nutrient-phytoplankton mini model with state pulse control was established.The existence of the first-order periodic solution and the condition of the asymptotic stability of the orbit are obtained by qualitative analysis of the model by means of the successor function and so on.In the fourth part,based on the nutrient-phytoplankton mini model,the switching system model is established.By means of Flippov system theory and convex method,the sliding mode region of the system and the sliding mode dynamics of the system in the sliding mode region are obtained.The global analysis of the dynamic behavior of the system is also carried out.