0 - 1 test for chaos

In 2004 Georg Gottwald and Ian Melbourne introduced a new test for chaos (Proc. Roy. Soc. A 460, 603–611). The input is any time series, that may come from a discrete map, a differential equation or an experiment. The output is a single number, which in theory is either 0, for non-chaotic data, or 1, for chaotic data. In practice, the result is close to 0 or close to 1, provided that enough data is used and provided that the input data is not over-sampled. The test has some advantages over other methods such as calculating Lyapunov exponents.

Z1TEST implements the 0 - 1 test as described in their most recent paper, "On the Implementation of the 0–1 Test for Chaos", available at http://arxiv.org/abs/0906.1418. To get good results you should have at least 1000 points. For continuous systems such as differential equations, you must be careful that the system is not oversampled. Roughly speaking, the graph of the data should not look smooth. Z1TEST incorporates two very basic checks to see if the series is oversampled and issues a warning if it is.