Self-organization of network dynamics into local quantized states

TL;DR

This paper demonstrates that complex localized patterns and cell assemblies in networks can spontaneously form through self-organization, modeled by a network analogue of the Swift-Hohenberg equation, without requiring reinforcement mechanisms.

Contribution

It introduces a minimal-ingredients network model inspired by the Swift-Hohenberg equation to explain the emergence of localized, robust cell assemblies in complex networks.

Findings

Network analogue of Swift-Hohenberg model produces localized patterns.

Self-organized cell assemblies form without synaptic reinforcement.

Localized structures serve as functional units in networks.

Abstract

Self-organization and pattern formation in network-organized systems emerges from the collective activation and interaction of many interconnected units. A striking feature of these non-equilibrium structures is that they are often localized and robust: only a small subset of the nodes, or cell assembly, is activated. Understanding the role of cell assemblies as basic functional units in neural networks and socio-technical systems emerges as a fundamental challenge in network theory. A key open question is how these elementary building blocks emerge, and how they operate, linking structure and function in complex networks. Here we show that a network analogue of the Swift-Hohenberg continuum model---a minimal-ingredients model of nodal activation and interaction within a complex network---is able to produce a complex suite of localized patterns. Hence, the spontaneous formation of robust operational cell assemblies in complex networks can be explained as the result of self-organization, even in the absence of synaptic reinforcements. Our results show that these self-organized, local structures can provide robust functional units to understand natural and socio-technical network-organized processes.