Local Lyapunov Exponents: Looking Closely at Chaos
本文介绍了状态依赖的有限时间局部李雅普诺夫指数，它能检测某些情况下的非线性，并作为诊断工具辅助判断混沌的存在。
SUMMARY When a deterministic mechanism gives rise to an erratic time series, then under certain conditions the series is said to exhibit chaos. The catalogue of statistical methods for the analysis of time series is being augmented currently by methods for the detection and quantification of deterministic chaos. A hallmark of chaos is the tendency of nearby trajectories to diverge in the short term. A measure of the average rate of exponential divergence exhibited by a chaotic system is given by the Lyapunov exponents of that system; the values of such exponents can suggest the presence of chaos. In this paper, we give a brief exposition of a finite time version of the Lyapunov exponent which is state dependent, and to which we attach the epithet ‘local'. The local Lyapunov exponent is shown to be able to detect non-linearity in some cases, and to have other qualitative features. As defined, its success is limited, but this does not preclude its usefulness as a diagnostic tool.