Spontaneous Formation of Dynamical Groups in an Adaptive Networked System

TL;DR

This paper studies an adaptive network model where coupled oscillators self-organize into two distinct dynamical groups with opposite phases, leading to a modular network structure with power-law distributed connection strengths.

Contribution

It introduces a model demonstrating spontaneous group formation and network modularity driven by coevolving dynamics and connections, revealing natural power-law distributions.

Findings

Oscillators form two groups with opposite phases.

Network evolves into a modular structure with strong intra-group links.

Connection strengths follow a power law distribution.

Abstract

In this work, we investigate a model of an adaptive networked dynamical system, where the coupling strengths among phase oscillators coevolve with the phase states. It is shown that in this model the oscillators can spontaneously differentiate into two dynamical groups after a long time evolution. Within each group, the oscillators have similar phases, while oscillators in different groups have approximately opposite phases. The network gradually converts from the initial random structure with a uniform distribution of connection strengths into a modular structure which is characterized by strong intra connections and weak inter connections. Furthermore, the connection strengths follow a power law distribution, which is a natural consequence of the coevolution of the network and the dynamics. Interestingly, it is found that if the inter connections are weaker than a certain threshold, the two dynamical groups will almost decouple and evolve independently. These results are helpful in further understanding the empirical observations in many social and biological networks.