Detecting chaos from time series

In this paper, an entirely data-based method to detect chaos from the time series is developed by introducing epsilon(P)-neighbour points (the p-steps epsilon-neighbour points). We demonstrate that for deterministic chaotic s ystems, there exists a linear relationship between the logarithm of the ave rage number of epsilon(P)-neighbour points, In n(p,epsilon) and the time st ep, p. The coefficient can be related to the KS entropy of the system. The effects of the embedding dimension and noise are also discussed.