The three-state test for chaos detection in discrete maps

The three-state test (3ST) – a new approach for chaos detection in discrete chaotic maps is presented. The scheme is based on statistical analyses of patterns obtained from ascending sorting of the system states. In addition to its ability for clear discernment between chaotic, quasi-periodic and periodic dynamical systems, the detection of periods of stable cycles is also automated with 3ST. The method is directly applied on data series generated by chaotic maps and does not require a priori knowledge of the equations of the underlying system. It also presents the advantage of not having to depend on the nature of the vector field as well as its dimensionality and is computationally low cost. The effectiveness of the 3ST is confirmed using two well known and widely studied chaotic maps: the logistic map and the Henon 2D map.