Complexity Measures from Interaction Structures

TL;DR

This paper introduces new complexity measures based on interaction structures to analyze symbolic dynamics, effectively identifying complex regimes in coupled systems like tent maps and cellular automata.

Contribution

It proposes novel complexity measures rooted in $k$-th order dependencies that improve the detection of complex dynamical behaviors.

Findings

Measures successfully identify complex regimes in coupled systems.

Measures capture higher-order interactions beyond pairwise dependencies.

Application to cellular automata demonstrates effectiveness.

Abstract

We evaluate new complexity measures on the symbolic dynamics of coupled tent maps and cellular automata. These measures quantify complexity in terms of $k$-th order statistical dependencies that cannot be reduced to interactions between $k-1$ units. We demonstrate that these measures are able to identify complex dynamical regimes.