The ‘ 0 – 1 test for chaos ’ and strange nonchaotic attractors

The ‘0–1 test for chaos’ due to Gottwald & Melbourne has been proved by them to distinguish robustly between periodic and low-dimensional deterministic chaotic dynamics. In this paper we apply the ‘0–1 test’ to a model 2D map exhibiting a transition between quasiperiodic dynamics and a strange nonchaotic attractor (SNA). The detection of a such a transition is a non-trivial numerical task since the Lyapunov exponent remains negative. We find that the ‘0–1 test’ successfully detects the transition, and we propose a simple modification of the standard implementation of the ‘0–1 test’ which considerably improves its ability to distinguish between the strange nonchaotic and purely quasiperiodic regimes. Our results indicate the practical usefulness of the ‘0–1 test’ for quasiperiodically-forced systems, and they show that the test offers a simple diagnostic method which is independent of any detailed knowledge of the underlying dynamics.