Unstable Dynamics, Nonequilibrium Phases and Criticality in Networked Excitable Media

TL;DR

This study investigates a networked excitable media model exhibiting unstable dynamics, nonequilibrium phases, and criticality, providing insights into neural and complex systems behavior through extensive simulations.

Contribution

It introduces a model demonstrating unstable and critical dynamics in excitable media, linking power-law distributions to critical states during system functionality.

Findings

Presence of 1/f noise in the system

Irregular wandering among attractors

Relation between power-law distributions and criticality

Abstract

Here we numerically study a model of excitable media, namely, a network with occasionally quiet nodes and connection weights that vary with activity on a short-time scale. Even in the absence of stimuli, this exhibits unstable dynamics, nonequilibrium phases -including one in which the global activity wanders irregularly among attractors- and 1/f noise while the system falls into the most irregular behavior. A net result is resilience which results in an efficient search in the model attractors space that can explain the origin of certain phenomenology in neural, genetic and ill-condensed matter systems. By extensive computer simulation we also address a relation previously conjectured between observed power-law distributions and the occurrence of a "critical state" during functionality of (e.g.) cortical networks, and describe the precise nature of such criticality in the model.