Information processing features can detect behavioral regimes of dynamical systems

摘要

In dynamical systems, local interactions between dynamical units generatecorrelations which are stored and transmitted throughout the system, generatingthe macroscopic behavior. However a framework to quantify and study this at themicroscopic scale is missing. Here we propose an 'information processing'framework based on Shannon mutual information quantities between the initialand future states. We apply it to the 256 elementary cellular automata (ECA),which are the simplest possible dynamical systems exhibiting behaviors rangingfrom simple to complex. Our main finding for ECA is that only a few featuresare needed for full predictability and that the 'information integration'(synergy) feature is always most predictive. Finally we apply the formalism toforeign exchange (FX) and interest-rate swap (IRS) time series data and findthat the 2008 financial crisis marks a sudden and sustained regime shift (FXand EUR IRS) resembling tipping point behavior. The USD IRS market exhibitsinstead a slow and steady progression which appears consistent with thehypothesis that this market is (part of) the driving force behind the crisis.Our work suggests that the proposed framework is a promising way of predictingemergent complex systemic behaviors in terms of the local informationprocessing of units.