Explosive synchronization transitions in complex neural network

TL;DR

This paper investigates how microscopic correlations between dynamics and topology influence explosive synchronization transitions in neural network models, revealing that network heterogeneity and degree correlations significantly affect transition nature.

Contribution

It demonstrates that degree-frequency correlation induces explosive synchronization in scale-free networks, while homogeneous networks exhibit continuous transitions, and degree assortativity suppresses explosive behavior.

Findings

Explosive synchronization occurs in scale-free networks with correlated frequencies.

Homogeneous Erdős-Rényi networks show continuous synchronization transitions.

Degree assortativity reduces the likelihood of explosive synchronization.

Abstract

It has been recently reported that explosive synchronization transitions can take place in networks of phase oscillators [G\'omez-Garde\~nes \emph{et al.} Phys.Rev.Letts. 106, 128701 (2011)] and chaotic oscillators [Leyva \emph{et al.} Phys.Rev.Letts. 108, 168702 (2012)]. Here, we investigate the effect of a microscopic correlation between the dynamics and the interacting topology of coupled FitzHugh-Nagumo oscillators on phase synchronization transition in Barab\'asi-Albert (BA) scale-free networks and Erd\"os-R\'enyi (ER) random networks. We show that, if the width of distribution of natural frequencies of the oscillations is larger than a threshold value, a strong hysteresis loop arises in the synchronization diagram of BA networks due to the positive correlation between node degrees and natural frequencies of the oscillations, indicating the evidence of an explosive transition towards synchronization of relaxation oscillators system. In contrast to the results in BA networks, in more homogeneous ER networks the synchronization transition is always of continuous type regardless of the the width of the frequency distribution. Moreover, we consider the effect of degree-mixing patterns on the nature of the synchronization transition, and find that the degree assortativity is unfavorable for the occurrence of such an explosive transition.