| This paper mainly studies a mathematical model that regulates the prey-predator system through state feedback pulse control to maintain balance and stability in polluted water environments.The dynamic analysis of the mathematical model is carried out using the relevant theory of pulse differential power systems,and the impact and biological significance of constant and pulse input on the dynamic system are discussed.The chapter 1 discusses in depth the background,research purpose and significance of this topic,introduces relevant knowledge of prey-predator systems,constant and pulse input,the application prospect and research status of pulse differential systems,and summarizes the research results of this paper.The chapter 2 introduces the basic concepts of semi-continuous dynamic systems,including their definitions and theorems,to provide powerful theoretical support for the research in the following chapters.In chapter 3,we study the pulse harvest problem of prey-predator systems with constant input in polluted water environments.First,a qualitative analysis of the unpulsed system is carried out,and then the pulse system is dynamically analyzed using the geometric theory knowledge of semi-continuous dynamic systems.The subsequent function method and the closed interval nesting theorem are used to prove the existence and uniqueness of the order-1periodic solution of the system,and the class Poincaré criterion is used to prove that the order-1 periodic solution of the pulse system is orbitally asymptotically stable.Finally,through numerical simulations,the conclusion is drawn and its biological significance is demonstrated.The chapter 4 further optimizes the adjustment strategy for state feedback pulse control of prey-predator systems based on the research in Chapter 3.The constant input is changed to pulse input,that is,the pulse control method is used to input the predator population.By analyzing the dynamics of the system and numerical simulation,it is verified that this method not only saves cost resources but also achieves greater economic benefits while maintaining the ecological balance of the water body.Finally,this paper provides a comprehensive summary and outlook of the research work,in the hope of achieving better results. |
