Symbolic dynamics analysis of chaotic time series with a driven frequency

A simple method to determine a partition line from chaotic time series with a driven frequency is devised, so that the embedded strange attractor can be divided effectively by the partition line. After the determination of grammatical rules, symbolic dynamics is established from the chaotic time series. The symbolic dynamics provides a global systematics of unstable periodic orbits within the strange attractor. With the global property, the symbolic dynamics is applied to find unstable periodic orbits and predict the chaotic time series with finite accuracy and symbolic sequences with high accuracy. © 1996 The American Physical Society.