Emergent explosive synchronization in adaptive complex networks

TL;DR

This paper introduces an adaptive network model with anti-Hebbian rules that leads to spontaneous explosive synchronization, shedding light on biological systems like brain networks where such phenomena occur.

Contribution

It proposes a novel adaptive network model coupling node dynamics with anti-Hebbian link evolution to explain explosive synchronization emergence.

Findings

Networks develop structural conditions for explosive synchronization

Anti-Hebbian adaptation induces inhibitory effects

Model explains biological phenomena like brain synchronization

Abstract

Adaptation plays a fundamental role in shaping the structure of a complex network and improving its functional fitting. Even when increasing the level of synchronization in a biological system is considered as the main driving force for adaptation, there is evidence of negative effects induced by excessive synchronization. This indicates that coherence alone can not be enough to explain all the structural features observed in many real-world networks. In this work, we propose an adaptive network model where the dynamical evolution of the node states towards synchronization is coupled with an evolution of the link weights based on an anti-Hebbian adaptive rule, which accounts for the presence of inhibitory effects in the system. We found that the emergent networks spontaneously develop the structural conditions to sustain explosive synchronization. Our results can enlighten the shaping mechanisms at the heart of the structural and dynamical organization of some relevant biological systems, namely brain networks, for which the emergence of explosive synchronization has been observed.