Emergent Macro-Criticality from Micro-Critical Agents

TL;DR

This study explores how collective critical-like behavior in multi-agent systems depends on the interplay between individual agent dynamics and the macroscopic interaction network structure, revealing that near-critical internal states alone are insufficient.

Contribution

It demonstrates that macroscopic criticality arises from the interaction network's properties and that microscopic regimes deviating from criticality can support collective near-critical behavior.

Findings

Near-critical internal dynamics alone do not produce collective criticality.

Effective connectivity of the interaction network controls activity propagation.

Subcritical micro-level regimes support wider near-critical macroscopic behavior.

Abstract

Criticality has been proposed as a key principle underlying complex behavior in biological and artificial systems; however, how criticality translates from individual dynamics to collective behavior remains unclear. We study this question using a multi-agent system with spatially constrained interactions in which agents sense neighboring light signals through exteroceptors and act by switching their own light on or off, thereby forming a dynamical interaction network at the macroscopic level. The agents' internal states are themselves governed by a reservoir dynamical system at the microscopic level. By varying the microscopic parameters around dynamical criticality, together with the macroscopic interaction topology, we systematically investigate the relation between the two levels. We find that near-critical dynamics within individual agents is not sufficient to produce collective critical-like avalanche statistics. Instead, scale-free behavior depends on the effective connectivity of the macroscopic interaction network, which controls activity propagation. As a result, macroscopic critical-like dynamics are enabled by microscopic regimes that deviate from criticality, with the required deviation depending on the properties of the interaction network. Investigating this relation, we find that slightly subcritical micro-level regimes support near-critical dynamics across a wider range of macroscopic parameters. These results show that in this multi-agent system, collective near-critical behavior depends on the interplay between internal dynamics and the interaction structure that governs activity propagation.