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中文摘要：
Lyapunov指数是标志一个系统做规则运动还是混沌运动的一个重要物理量.鉴于此,本文利用Lyapunov指数研究系统的混沌特性,研究气候的突变.计算结果表明,定义法求得的Lyapunov指数是一种可靠的突变检测方法,无论是理想序列还是实际存在突变的序列,利用该方法都能准确地找出突变位置;而利用非线性局部Lyapunov指数的可预报期限从理论上佐证了基于临界慢化现象的气候突变前兆信号的可靠性,通过计算各个时间段的最大Lyapunov指数能够反映系统的内在性质、研究其混沌特性.研究结果为该方法在实际观测资料中的广泛应用提供了理论基础.
英文摘要：
Lyapunov exponent is an important physical quantity indicating a system is in regular motion or in chaotic motion. In view of this, in this paper, we use the Lyapunov exponent to study the chaotic properties of the system, and the mutations in climate. The results show that the Lyapunov exponent is a reliable mutation detection method. For the ideal sequence or actual atmosphere sequence the method can be used to accurately find out the mutation position; the predictability of nonlinear local Lyapunov exponent is used to evidence the reliability of the early warning signals of abrupt climate change based on the phenomenon of critical slowing down, through calculating the largest Lyapunov exponent of each time the system intrinsic properties can be reflected and the chaos characteristics can be studied, thereby providing a theoretical basis for the wide applications of the present method in real observation data.
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