Detecting chaos from time series

Abstract

In this paper, an entirely data-based method to detect chaos from the time series is developed by introducing ∈p-neighbour points (the p-steps ∈-neighbour points). We demonstrate that for deterministic chaotic systems, there exists a linear relationship between the logarithm of the average number of ∈p-neighbour points, ln np,∈, and the time step, p. The coefficient can be related to the KS entropy of the system. The effects of the embedding dimension and noise are also discussed.