Research On The Stability And Convergence Rate Of Several Types Of Time-delay Dynamic Systems

Considering the influence of the past on the current state,the time-delay differential equation represents the developing system which relies on the current state and the past state at the same time,it has a wide range of applications in biology,engineering,economics and other fields,so it is particularly important to study the dynamic behavior of the delay dynamic system with practical application background.Based on the basic theory of delay differential equation,this paper applies the geometric stability switches criteria to study the stability convergence rate of several kinds of delay dynamic systems.Firstly,a kind of organic chemostat model with time delay is studied.In this paper,the convergence rate of the model,namely stability and ?-stability,is studied by using the geometric stability switches criteria in delay differential equations,and the corresponding stability region is calculated and where the hopf bifurcation is generated,it shows the distinction and connection between stability and ?-stability,and numerical simulation proves the practicability and feasibility of the theoretical analysis.Secondly,the fluid flow congestion model with time delay is studied.In this paper,an improved fluid flow congestion model is constructed by adding communication delay into the traditional network congestion model,the convergence rate of this model,namely stability and ?-stability,is studied by using the geometric stability switches criteria in delay differential equations,and the corresponding stability region is calculated and where the hopf bifurcation is generated,it shows the distinction and connection between stability and ?-stability,at the same time,numerical simulation proves the practicability and feasibility of the theoretical study.Finally,the advertising sales model with time delay is studied.In this paper,time delay is added into the traditional advertising sales model to build an advertising sales model with time delay,the convergence rate of this model,namely stability and?-stability,is studied by using the geometric stability switches criteria in delay differential equations,and the corresponding stability region is calculated and where the hopf bifurcation is generated,it shows the distinction and connection between stability and ?-stability,and the validity of theoretical analysis is verified by numerical simulation.