Study Of Nonlinear Dynamics And Analysis Of Stochastic Gradient Boosting In Price System

With the global economy integration, the factors affecting the economy and the relations of the factors become more complex, which is most marked in the price system. As the traditional economic theory cannot describe them, nonlinear economics become the research focus and have made rapid progress. This dissertation studies the price operation phenomenon in the property prices system with the aid of modern nonlinear dynamics and stochastic dynamics theory. The main content is as follows:Summarize several prices models systemically: summarize the origination, application condition, consumptions of cobweb price model, introduce the discrete case and continuous case of the model, evaluate the application of the cobweb theory, the linear difference model of dynamic linear price models, linear price model in stock, linear differential equation price model as well as nonlinear dynamic price model have been studied. On the basis of the above models, a nonlinear dynamic price model is set up considering the nonlinear factors between supply and demand. And the meanings of each parameters of the model have been explained.Based on the nonlinear dynamic price model considering supplier and retailer, the system stable theory has been obtained from the analysis of the model using nonlinear dynamics; after numerical simulating of the model with MATLAB, present the influence of different parameters on the system stable has been obtained, in which the influence of the parameters on the system conditions has also been considered.First introduce the basic theory of random dynamical system, stochastic averaging method, stochastic differential equation, the stability of random dynamical system, calculation of Lyapunov exponent, the boundary analysis of one-dimension diffuse and the probability density function calculation of two-dimension Markov stochastic process. Then present a nonlinear random price model: the stability condition of the model is figured out through stability analysis. The stochastic Hopf bifurcation behavior and the economic significance of the system have been studied.Analyze the composition of property price and the main factors influencing the price fluctuation in the market price system which is influenced by the police, then analyze the actual datum of the property in Tianjin, Shijiazhuang, Nanjing and Zhengzhou by stochastic gradient regression method, present the influences of each main factors to the price change in Tianjin, Shijiazhuang, Nanjing and Zhengzhou, forecast the property price prospect in these cities by the method also.