Dynamics Of A Predation Model With State Dependent Impulsive Effect

For a long time,how to deal with the interspecific relationship has always been accompanied by the development of human civilization.Since the emergence of human civilization,the relationship between human and nature has become particularly important.The emergence of population dynamics has provided great help to solve the problems between populations and deal with the interspecific relations.The mathematical model of dynamics can better describe the basic relations such as predation,competition,symbiosis,parasitism and so on.Among them,the predatorprey relationship is one of the most basic and important relationships.The predator will try their best to kill prey and prey avoid hunting in order to survive,and many complex diffusion phenomena will occur in this process.Therefore,this paper considers the influence of several factors on the predator-prey relationship in the population,and analyzes the predator-prey model.In the second chapter,we introduced the basic predator-prey model.The existence and types of equilibrium points of the model are discussed without considering time delays and impulses.By analyzing its dynamic properties,conditions for the stability of the equilibrium point are given,and the existence of limit cycles is discussed.The phase diagram is given by numerical simulation.In the third chapter,we proposed an integrated control method for pests.Based on the predator-prey basic model,a state impulsive feedback control with stage structure is established.An integrated control strategy for pests is proposed.The existence and uniqueness of the order-1 periodic solution are proved using the successor function method,and the feasibility of biological and chemical control strategies for pest management is verified.Secondly,the stability of the system is proved through Hurwitz criterion and numerical simulation.Finally,through numerical simulation,it is found that the model has stable order-1 periodic solution,and high order periodic solution phenomena occur.In chapter four,a class of predator-prey model with nonlinear state feedback control is established,and its complex Poincare map is analyzed in detail,including its continuity,discreteness and impulsive dynamics properties.The possible existence of multiple fixed points is discussed,and the existence of supercritical bifurcation is also analyzed,and the above cases are simulated with MATLAB.In chapter five,we proposed a pulse control system with active thresholds,in which the control intensity and control range of pests will play an important role in the final control effect.Through the analysis of the Poincare map,we obtained the existence of periodic solutions is obtained,and the precise pulse sets and phase sets of the model by discussing various pulse sets and phase sets.