一类非线性金融系统的数值研究  

NUMERICAL STUDY OF A CLASS OF NONLINEAR FINANCIAL SYSTEM

作　　者：凯歌 张伟[1] 

机构地区：[1]北京工业大学机电学院,北京100124 [2]内蒙古财经大学统计与数学学院,呼和浩特市010070

出　　处：《动力学与控制学报》2016年第5期407-411,共5页Journal of Dynamics and Control

基　　金：内蒙古自治区高等学校科学研究项目(NJZY134);内蒙古财经大学校级科研项目(KY1306)~~

摘　　要：利用数值模拟的方法研究了一类非线性金融系统的动力学行为.建立了由生产、资金、股份、劳动力四个部分构成的一类非线性金融系统的动力学模型.首先运用四维微分方程来描述由利率、投资需求、价格指数和平均利润率构成的四个状态变量随时间的变化,然后将金融系统简化为四维自治微分方程组.通过对四维自治微分方程组进行数值模拟发现了非线性金融系统的动力学特性,从数值模拟获得的三维相图反映了金融系统的非线性特性.从数值模拟结果发现,在特定的条件下非线性金融系统存在周期运动和混沌运动.除此之外,还观察到参数的改变对四维自治金融系统的非线性特性有着显著的影响.In this paper, the dynamic characteristics of a class of nonlinear finance system are investigated by means of numerical simulation. The model developed in this work is composed of four sub-blocks： production, money, stock and labor force. At first, the development of four state variables for the interest rate, the investment demand, the price exponent, and the average profit margin with the time are described by four dimensional differ- ential equations. The hyper chaotic finance system is simplified as a group of four dimensional autonomous differ- ential equations. The nonlinear dynamic characteristics of the system are then examined by the numerical simula- tions of four dimensional differential equations. The three-dimensional phase diagrams illustrated the nonlinear characteristics of the financial system. Moreover, the numerical results demonstrated that under certain condition, periodic motion and chaotic motion exist in the nonlinear system. In addition, it is found that system parameters and initial conditions have great influence on the nonlinear dynamical behavior of four dimensional autonomous hyper chaotic systems.

关 键 词：非线性经济学 混沌金融系统 复杂的动力学行为 混沌运动 经济动力学 

分 类 号：F224[经济管理—国民经济] F830