Global Dynamics Analysis Of Two Kinds Of Non-smooth Biological Models With Time Delay Control

Differential equations are an important mathematical theory for studying the laws of motion and evolution of things and phenomena in nature and society.The mathematical model of differential equations plays an important role in describing the dynamic behavior of biological models.Considering the implementation of the strategy,this paper studies the global dynamics analysis of two types of non-smooth biological models with time delay control,focuses on the changes of the system under time delay perturbation,and gives some solutions-The full text consists of the following four parts.The first chapter summarizes the research background,significance,and development status of the biological models considered in this paper.Compared with the general biological model,the dynamic system with time delay is more in line with the actual production and life needs.In addition,this chapter elaborates on a series of problems posed by the la.g in joining the system for the study of such systems.Then we introduced the main content of our research.The second chapter,some preliminary knowledge required for this article,briefly introduces the Flippov system,including the definition of the solution and the Filippov solution of the differential equations.Secondly,some basic knowledge of functional differential equations is described,and the definition of Filippov solutions in the context of functional differential equations is elaborated.On this basis,the theory of Lyapunov stability of Filippov system and the basic basis for judging the stability of functional differential inclusions.In addition,this chapter also deals with subsystems and equilibrium points of the Filipov system.In the last subsection of this chapter,an invariant principle is highlighted.In the third chapter,a type of fishery fishing model under time lag control is studied.The generalized Lyapunov method proves the global asymptotic stability of each equilibrium point.In particular,when the equilibrium points are all imaginary equilibrium points,the existence of periodic solutions under time delay disturbance.In the fourth subsection of this chapter,the experimental results of numerical simulation verify the accuracy of the results in this paper.In the fourth chapter,we first describe the background of the SQIR model with time delay,and establish the existence and global stability of the equilibrium point through the generalized Lyapunov method.In addition,combined with the Poincaremapping,the displacement function,and the Melnikov method,we derive some sufficient conditions to ensure the existence,uniqueness and global stability of the periodic solution of slow oscillation.At last,we summarize our research work and look forward to the future research direction.