The Research Of Stochastic Stability And Bifurcation Of Non-linear Economical Period Model

With the global economy integration, the factors affecting the economy and the relations of the factors become more complex. The traditional economic theory cannot describe it, but nonlinear economics (chaotic economics) has become the research focus, and made rapid progress. This dissertation studies the complex nonlinear phenomenon in the economic system with the aid of modern nonlinear dynamics and stochastic dynamics theory. The main content is as follows:1 The Hicks'consumption function model was improved, the Puu's investment function model with cubic nonlinearity was introduced, and the nonlinear economic period model of social economic system was set up when the effect of periodic fluctuation on economic system was considered. The nonlinear dynamic characteristic and stability of that system was studied, three kinds of social economic form was divided, and the risk in transform process between different economic forms was analyzed. Finally the theoretic results were proved by numerical simulation.2 A stochastic economic period model considering the stochastic independence function is set up. The complete stable condition has been obtained with Lyapunov exponent based on multiplicatibve ergodic theorem and boundary analysis of one-dimension diffuse process to this weak damp and weak stimulation Quanti-non-integrate Hamiltion system. The stochastic Hopf bifurcation behavior has been studied on the basis of joint probability density and marginal probability density under different parameters condition, and validated with the numerical simulation.3. For hourly telephonometry within the busiest period in one day of Xiqing, Tianjin, the optimal embedding dimension and delay time were determined by false nearest neighbors and Cao's method. The predicted errors of preserved 300 records were calculated by random forest, stochastic gradient boosting, support vector and artificial neuron network. The results show that artificial neuron network predict the most precisely.