Study Of Stochastic Bifurcation And Chaotic Phenomenon In Economic System

With the global economy integration, the factors affecting the economy and therelations of the factors become more complex. The traditional economic theorycannot describe it, but nonlinear economics (chaotic economics) has become theresearch focus, and made rapid progress. This dissertation studies the complexnonlinear phenomenon in the economic system with the aid of modern nonlineardynamics and stochastic dynamics theory. The main content is as follows:1. Summarize the western business cycle theory systemically, based on theHicks' consumption model and Puu's investment model with cubic nonlinearity, setup the dynamic nonlinear business cycle model, considering the nonlinear accelerator.Apply the modern nonlinear dynamics to analysis the dynamic behavior of the model,found that under different parameters three types of bifurcation occured: Hopfbifurcation, supercritical and subcritical furcation bifurcation. Analysis the bifurcationparameters and validate with the numerical simulation.2. First set up a stochastic business cycle model considering the stochasticindependence function. Gain the complete stable condition with Lyapunov exponentbased on multiplicatibve ergodic theorem and boundary analysis of one-dimensiondiffuse process to this weak damp and weak stimulation Quanti-non-integrateHamiltion system. Study the stochastic Hopf bifurcation behavior on the basis of jointprobability density and marginal probability density under different parameterscondition, and validate with the numerical simulation.3. Based on the conception of false nearest neighbor, which determines the bestembedding dimension m and time delay Ï„ simultaneously, reconstruct the practicaleconomic time series. Demonstrate the practical economic time series with the maxLyapunov exponent, fractal dimension and Kolmognov entropy, present severalchaotic validation method, validate the accuracy of the parameters selection of phasereconstruction, find out the chaotic property, and figure out the max predictable scale.4. On the basis of the max predictable scale, which is the reciprocal of the maxLyapunov exponent, set up a genetic neural network of [1/LE] input nerve cells. Thisalgorithm can work out the best topologic structure of the network automatically, andget the global optimization. Demonstrate with the practical economic series, andcompared with the common predictive method of chaotic time series: phaseprediction, local prediction and artifical neural network, and find out that all the fourmethod is satisfactory with the mean error of 3%, genetic neural network offers moreaccurate result of mean error within 2%.