| The sustainable development and utilization of fishery resources depend on the stock and aquatic products of animals and plants.The survival and growth of aquatic animals and plants are not only related to the eco-logical environment of the water,but also to people’s development capabilities.Frequent water pollution and human overdevelopment are the important factors that affect the sustainable development of fishery resources.Therefore,this paper not only considers the biological control measures of water environment,but also the development of target income when constructing the model.Given that the management measures are of pulse and phase,a variable structure model,a differential algebra model and a pulse model are established based on a class of fishery model with nutrient cycling.This paper can be divided into four parts.The first part mainly introduces the fishery resources,the research status of the fishery ecosystem,the present situation of water pollution and the treatment methods.Then the definition of relevant mathematical models and some relevant knowledge of preparation are introduced.The second part establishes a kind of fishery management model of variable structure,in consideration of the stage harvest of algae,including continuous harvesting model and harvest strategies along with the change of resource stock model.The existence and stability and branches of the equilibrium state are discussed respectively.The persistent proof train of thought of the variable structure of fishery model is given.The third part sets up a model of differential algebraic fishery management with a certain economic target profit,considering the fact that managers require a certain economic benefits.With of help of Hurwitz criterion and Jacobian matrix,etc,the author discusses the existence and stability of the equilibrium system.Hopf branch theorem is used to discuss the branch of economic equilibrium.In the fourth part,the pulse model with quadratic pulse effect is established considering that the collection of algae and the occurrence of fish happen at different moments in the process of controlling water.The existence and stability of the boundary equilibrium point are discussed by Floquet theory.And then the relevant discussion of the persistence and the corresponding threshold are given. |
