Dynamics Research Of A Predator-Prey Model With A Predatory Population Affected By Toxins

A population model is a mathematical model that describes group behavior.It can be used to study the complex behavior within a group and the interaction between the group and the external environment.The model is beneficial for predicting and simulating large-scale biological systems that cannot be tested on computers.Therefore,population models are an essential research tool in ecology.In this thesis,the stability of the ordinary differential equation and the theory of impulsive differential equation is used to study the dynamic properties of the predator-prey model in which the predator-prey population is affected by toxins.Chapter 1 mainly elaborates on the background,significance,and purpose of this research topic,introduces the development background and current research status of impulsive differential equations,and then provides detailed preliminary knowledge such as the primary definition and main lemmas of semi-continuous dynamic systems used in the argumentation process of this article,laying a theoretical foundation for subsequent population model research and analysis.Chapter 2 establishes a predator-prey model with a constant feeding rate of predators under the influence of toxins.The existence of the equilibrium point and the stability of the positive equilibrium point of the system is studied,combined with the theory of pulsed differential equations.The pulse control of the pulseless system is carried out according to the actual situation,the persistence of the predation system is discussed,and the uniqueness of the order 1 periodic solution of the system is proved by the following function method and interval set theorem,and finally;the conclusion is verified by numerical simulation.In Chapter 3,a predator-prey model with the sudden release of prey under the influence of toxins was established,and the global dynamics of impulsive free systems were analyzed using methods such as Bendixson Dulac theorem and Poincar é-Bendixson theorem;Then,the existence and uniqueness of the order 1 periodic solutions under different conditions were proved;Secondly,using the Poincar é criterion,the requirements for the stability of the order1 periodic solution are obtained;Finally,different pulse coefficients,thresholds,and toxin coefficients were selected to discuss the impact of various parameters on the sustainable development of fish.Finally,numerical simulation results verified the rationality of the conclusion.