Phenomenology of coupled non linear oscillators

TL;DR

This paper investigates the complex patterns and information processing capabilities of a ring of coupled nonlinear oscillators using entropic measures, revealing behaviors similar to cellular automata and analyzing system stability and parameter effects.

Contribution

It introduces a detailed analysis of coupled nonlinear oscillators' information dynamics using Lempel-Ziv entropy and stability measures, extending cellular automata concepts to continuous parameter spaces.

Findings

Complex spatial and temporal patterns resemble cellular automata behaviors.

System stability varies with initial conditions and control parameters.

Density of digits over time provides insights into system dynamics.

Abstract

A recently introduced model of coupled non linear oscillators in a ring is revisited in terms of its information processing capabilities. The use of Lempel-Ziv based entropic measures allows to study thoroughly the complex patterns appearing in the system for different values of the control parameters. Such behaviors, resembling cellular automata, have been characterized both spatially and temporally. Information distance is used to study the stability of the system to perturbations in the initial conditions and in the control parameters. The latter is not an issue in cellular automata theory, where the rules form a numerable set, contrary to the continuous nature of the parameter space in the system studied in this contribution. The variation in the density of the digits, as a function of time is also studied. Local transitions in the control parameter space are also discussed.