The Building And Qualitative Analysis Of Third-party Payment Platform Model

The study on natural ecosystem of biologic population model is the important topic of differential equations. The relevant academic researches such as epidemics are based on natural ecosystem and power systems discussed. According to the qualitative and stability theory of differential equations, here we mainly research the competition model of a third-party payment platform with delays.Tian constructed a mathematical model to describe the interaction between the enterprises of the business ecosystem with the relevant economics theoretical in 2006. Basing on the natural ecosystem and business ecosystem, we first define the system on the third-party payment platform as e-payment systems. where the ecosystem based on the natural ecosystems and commercial Eco-system, and initially establish the interaction model among third-party payment. According to the related concepts of natural ecosystem,interactive model of third-party payment established between the coefficients given economic sense.Xu studied the periodic behavior of the two companies competing models via mathematical methods in the coincidence degree theory in 2012. Liao studied on the model of a single delay research. In this paper, a new model based Liao is established, according to the understanding and theoretical definition of third-party payment platform. Form a mathematical model, the establishment of third-party payment platform competing models with two delays, we analysised the relationship between the third-party payment platform; Then discussed when the two delay is not same, the stable of the unique positive equilibrium and Hopf bifurcation; Finally, through the center manifold and normal form theory to obtain the two delays are present in nature and does not equal under the system of bifurcation.Through these studies, we can establish a simple third-party electronic payment competition model and calculate its positive equilibrium and Hopf bifurcation, then compare the advantages and disadvantages of competition model and competition and cooperation model.