Neimark-Sacker Bifurcation Analysis Of Three Kinds Of Discrete-time Internet Congestion Models With Delay

With the rapid development of computer network,it has become an indispensable part of people's life,so it is of great practical significance to study the behavior and stability analysis of computer interent in congestion.In this dissertation,the stability and bifurcation of three kinds of discrete-time internet congestion models with time delay are analyzed and discussed:Firstly,the stability and bifurcation of a class of discrete internet congestion models with delay are studied.When the delay in the model is taken as the bifurcation parameter,the Neimark-Sacker Bifurcation will be generated when the bifurcation parameter passes through a set of critical values.That is to say,with the change of the bifurcation parameter,the stability of the congestion model at the fixed point will change.The results are verified by numerical simulation.Secondly,a negative feedback term is added to the discrete congestion model with time delay,and the stability of the discrete congestion model is studied.In this paper,we obtain the conditions for generating the Neimark-Sacker Bifurcation of the model,and apply the central manifold theorem and the normal form theory to study the direction of the Neimark-Sacker Bifurcation and the stability of the bifurcation invariant closed curve.The results are verified by numerical simulation.Finally,in order to control the bifurcation of the internet congestion model,the dynamic feedback model is added to the original internet congestion model to form a two-dimensional interent congestion model.The stability of the discrete model of this kind of two-dimensional interent congestion model is studied.When the delay is taken as a parameter,the discrete model of congestion model generates Neimark-Sacker Bifurcation near the Hopf Bifurcation when the Hopf Bifurcation is generated at the bifurcation parameter value.