Two Predator-Prey Modeles With State-Dependent Feedback Control

As an important social behavior,"herd behavior" not only plays an important role in the survival and evolution of the predator,but also plays a very important role in the predator's predation competition.Therefore,this thesis considers the mathematical model in which only the predator behaves "herd behavior" and the mathematical model in which both the predator and the predator exhibit "herd behavior",both of them have important significance and good application value in studying the evolution and dynamic balance of predators and prey.Constructing a predator-prey model with a single square root response function and state-dependent feedback control based on the situation that only the predator performs "herd behavior";using the differential equation geometry theory and the semi-continuous dynamic system theory,the number of equilibrium points of the models under different conditions is studied,and the different types of the equilibrium points are studied without implementing control;the existence of the order-periodic solution in the case of implementing a pulse is discussed by using the successor function method for different conditions,and the sufficient conditions for the existence of the order-1 periodic solution are obtained and verified by numerical simulation.Constructing a predator-prey model with double square root response function and state-dependent feedback control based on the situation that both the predator and the predator exhibit "herd behavior",particularly,a model that does not contain the average time-consuming factor of the predator during the predation process was studied;using the differential equation geometry theory and the semi-continuous dynamic system theory,the number of equilibrium points of the models under different conditions is studied,and the different types of the equilibrium points are studied without implementing control;the existence of the order-periodic solution in the case of implementing a pulse is discussed by using the successor function method for different conditions,and the sufficient conditions for the existence of the order-1 periodic solution are obtained and verified by numerical simulation.The research results enrich the theory of state-dependent feedback control in biomathematics and provide a certain decision basis for the implementation of human interference in real life.