【作者】 方文轩；

【导师】 王洪礼；

【作者基本信息】 天津大学 ， 工程力学， 2007， 博士

【摘要】 随着全球经济一体化进程的深入,影响经济运行的因素以及这些因素之间的关系更加复杂,传统的经济学理论已无法准确描述,非线性经济学(或混沌经济学)已逐渐成为当代经济学研究的前沿领域,并已取得迅速的进展。本文运用现代非线性动力学理论与随机动力学理论,研究了经济系统中复杂非线性现象的运行规律,并对实际经济序列进行了实证研究,主要完成了以下工作:1、建立了社会经济动力学系统的非线性经济周期模型;分析了具有周期激励的社会经济动力系统的稳定性,并通过边界划分将社会经济发展形态划分为三种不同的类型,具体研究了我国在计划经济时代与西方发达国家在经济表现方面的差异,指出了社会转型时期可能面临的风险及风险源。结果表明投资加速数ν与边际储蓄倾向s之差a的变化,是引发社会经济系统发生分岔行为的主要因素,并通过数值仿真验证了理论结果。2、首先考虑了具有随机形式的自主函数,建立了随机经济周期模型;由于该系统是弱阻尼弱激励的拟不可积Hamilton系统,因此运用基于乘积遍历性定理的Lyapunov指数及一维扩散过程的边界分析理论,得出该系统的局部稳定性和全局稳定性条件;根据系统响应联合概率密度和平稳概率密度以及不同的参数条件,研究了该模型的随机Hopf分岔行为,并对分岔参数进行了具体分析,还通过数值仿真进行了验证。3、采用基于虚假最近领域概念以及Cao方法,确定天津市西青区每天最忙时段话务量最佳的嵌入维数和时间延滞。并用随机森林、随机梯度Boosting、支持向量机和人工神经网络四种算法对预留的数据进行了预测,结果表明人工神经网络的预测误差最小。更多还原

【Abstract】 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.更多还原