Dynamic Analysis Of Websites Competition Model With Multiple Delays

In this dissertation,a multi-delay websites competition model with self-feedback delay,competition delay and network congestion feedback delay is studied.The following research work has been done to explore the competition law among websites in the Internet market competition environment by applying the mathematical theory of delay differential equation and the method of computer numerical simulation.Firstly,the local stability and the sufficient conditions for the existence of Hopf bifurcation of the websites competition model with both self-feedback delay and competitive delay are proved by analyzing the characteristic equation at the positive equilibrium point.Then,the direction of Hopf bifurcation and the stability of periodic solution of the model are discussed by using the canonical form and the central manifold theorem.Finally,the correctness of conclusions of this chapter are verified by the numerical simulation.Secondly,through assuming that the growth rate and competition coefficient of page views of websites are positive periodic functions,a non-autonomous dual-delay websites competition model is established.Firstly,two lemmas are introduced to discuss the extinction and uniform persistence of the model.Secondly,the existence of positive periodic solutions of the model is studied by using the Mawhin coincidence degree theory.Finally,the conclusions of this chapter are verified by numerical simulation.Thirdly,considering the influence of network congestion feedback delay on websites competition model,a kind of websites competition model with self-feedback delay,competition delay and network congestion feedback delay is proposed.The local stability and the sufficient conditions for the existence of Hopf bifurcation are proved by analyzing the characteristic equation at the positive equilibrium point of the multi-delay websites competition model.Furthermore,sufficient conditions for global asymptotic stability of the model are obtained by constructing appropriate Lyapunov functional.Finally,the correctness of conclusions of this chapter are verified by the numerical simulation.