基于混沌理论的上海股市非线性动力学研究

Research on Non-Linear Dynamics Characters of Shanghai Stock Market Based on Chaos Theory

介绍了资本市场的非线性动力学方法,使用重构相空间技术重构了上海股市的相空间,描述了其二、三维演化趋势图,并分别计算了关联维数,得到了它的饱和嵌入维数,说明上海股市是具有分数维结构的低自由度混沌系统,计算了最大Lyapunov指数。通过计算表明,上海股市是混沌系统,进一步解释了上海股市非线性复杂性形成的机理。

This paper firstly introduces non-linear dynamics model of the capital market. Then, we reconfigure the phase space of Shanghai stock market by using reconfiguration phase space technology, and picture its 2-dimension and 3-dimension trend charts. We also calculate the correlation dimension of Shanghai stock market, and find its saturated embed dimension that demonstrates that Shanghai stock market is a low-freedom chaos systems which has a fractional dimension structure. Finally, we calculate Lyapunov exponent of Shanghai stock market, and find its value is greater than zero, which demonstrates that Shanghai stock market is a chaos system that further interprets mechanics of forming non-linear complexities of Shanghai stock market.