Contrasting chaos with noise via local versus global information quantifiers

At issue here is the distinction between noise and chaos. They are different phenomena but sometimes produce results that resemble each other. From a numerical viewpoint, in particular, subtle differences that exist between them are often difficult to discern. We present here a conceptual scheme, based on Information Theory, that successfully distinguishes between these two regimes. The idea is to look for the location of the pertinent signal on a special plane, called the information-one, whose axes are entropic-like measures. Using these quantifiers (one local, the other global), the contrast between the two dynamical regimes becomes apparent.

► Distinctions between noise and chaos represented by time series are studied.
► A scheme, based on Information Theory tools is presented.
► The Bandt–Pompe approach for associating PDFʼs to time-series is used.
► The causality Shannon–Fisher information plane is introduces.
► Using this plane, the two dynamical regimes become apparent.