Effect of assortative mixing in the second-order Kuramoto model

TL;DR

This study investigates how assortative mixing influences the synchronization transition in the second-order Kuramoto model on scale-free networks, revealing controllable collective dynamics through network and damping adjustments.

Contribution

It demonstrates that assortativity affects the nature of synchronization transitions in the second-order Kuramoto model, and shows how damping can compensate for these effects.

Findings

Discontinuous transitions occur in both assortative and disassortative networks.

Adjusting phase damping can offset the effects of assortativity on synchronization.

Network structure and damping parameters can be tuned to control collective oscillator behavior.

Abstract

In this paper we analyze the second-order Kuramoto model presenting a positive correlation between the heterogeneity of the connections and the natural frequencies in scale-free networks. We numerically show that discontinuous transitions emerge not just in disassortative but also in assortative networks, in contrast with the first-order model. We also find that the effect of assortativity on network synchronization can be compensated by adjusting the phase damping. Our results show that it is possible to control collective behavior of damped Kuramoto oscillators by tuning the network structure or by adjusting the dissipation related to the phases movement.