Time-series analysis of transient chaos

A time-series analysis method of transient chaos is worked out which can also be applied to signals of laboratory experiments and is illustrated and its validity is checked by the H\'enon map.

Abstract

A time-series analysis method of transient chaos is worked out which can also be applied to signals of laboratory experiments. The process is based on the construction of a long artificial time series obtained by gluing pieces of many transiently chaotic signals together. This artificial signal represents a long-time motion in the vicinity of the nonattracting chaotic set. Thus all of the well-known numerical methods developed for analyzing permanent chaotic behavior are applicable in a more convenient way than using many short separated time-series pieces. The method is illustrated and its validity is checked by the H\'enon map. The nonattracting strange set is reconstructed in the presence of both a periodic and a chaotic attractor, and quantitative characteristics such as dimensions and Lyapunov exponents are determined by means of time-delay embedding methods.