金融危机传染的非线性动力学模型

越来越多的证据表明全球金融市场是高度复杂,广泛联接的非线性动力系统网络,由于系统的非线性和复杂性特征使得金融危机极易通过系统间的耦合作用而发生传染.针对金融危机传染所表现出的非线性动力学特性,本文构建了以传染源国家和受传染国家股票收益率为变量的微分动力学传染模型.利用微分方程定性理论对模型的奇点进行讨论,得出极限环存在的条件及形式,并进而得出金融危机传染的三种情况:轻度传染、可控传染和强烈传染.

A Nonlinear Dynamic Model of Financial Contagion

The increasing evidences have proved that the financial market is a multi-level nonlinear dynamical system constituted by financial subsystems coupled with extensive connections,which easily transmits the contagion instantaneously. Employing the Differential Dynamics Method,a nonlinear dynamic model was set up to describe the international financial crises contagion within a short time between two countries.The two countries＇control force depends on the timely financial assistance,the positive attitude and actions to rescue the other infected countries,and investor confidence aggregation,and the immunity ability of the infected country is considered as the major reasons to drive the nonlinear fluctuations of the stock return rates in both countries during the crisis.According to the Ordinary Differential Equations Qualitative Theory,we find that there are three cases of financial crisis contagion within a brief time between two countries：weak contagion with instability but inhibition,contagion with limit and controllable oscillation,and strong contagion without control in a brief time.