The Geometric Criterion Method Is Used To Study The Stability And Convergence Rate Of Delay Differential Equations

Delay differential equation is a differential equation with time lag.It is used to describe the development system that depends on both current and past states.It has important applications in the fields of physics,mechanics,control theory,biology,medicine and economics due to the full consideration of the influence of history on the current state.The bifurcation problem is usually used to study the structural instability of nonlinear systems,and it is an important subject in differential equations.The study of stability and bifurcation of delay differential equations is of theoretical and practical significance.In this paper,we study the application of delay differential equations in biological and economic models.In the first chapter,we introduce some basic definitions and theorems and methods of delay differential equations.In Chapter 2,we study the stability and stability of the dynamic system for continuous culture of microorganisms with time delay,that is,the convergence rate of stability.By using the geometric switching method for stability of delay differential equations,we find the convergence interval and where to generate Hopf bifurcation.Finally,the correctness and effectiveness of the conclusion are verified by numerical simulation.In Chapter 3,we study the stability and stability of the dynamic system of continuous culture of microorganisms with time delay,that is,the convergence rate of stability.By using the geometric switching method for stability of delay differential equations,we find the convergence interval and where to generate Hopf bifurcation.Finally,the correctness and effectiveness of the conclusion are verified by numerical simulation.In Chapter 4,we study the stability and stability of the dynamic system for continuous culture of microorganisms with time delay,that is,the convergence rate of stability.By using the geometric switching method for stability of delay differential equations,we find the convergence interval and where to generate Hopf bifurcation.Finally,the correctness and effectiveness of the conclusion are verified by numerical simulation.