Collective synchronization in the presence of reactive coupling and shear diversity

TL;DR

This paper investigates how reactive and dissipative couplings influence synchronization in a complex oscillator model with heterogeneity, revealing that shear diversity can prevent synchronization unless reactive coupling dominates.

Contribution

It provides exact analytical results on the effects of reactive and dissipative couplings on synchronization thresholds considering shear and frequency heterogeneity.

Findings

Shear diversity prevents synchronization in dissipative coupling.

Reactive coupling allows synchronization depending on shear mean.

Synchronization threshold depends on shear distribution mean, not all moments.

Abstract

We analyze the synchronization dynamics of a model obtained from the phase reduction of the mean-field complex Ginzburg-Landau equation with heterogeneity. We present exact results that uncover the role of dissipative and reactive couplings on the synchronization transition when shears and natural frequencies are independently distributed. As it occurs in the purely dissipative case, an excess of shear diversity prevents the onset of synchronization, but this does not hold true if coupling is purely reactive. In this case the synchronization threshold turns out to depend on the mean of the shear distribution, but not on all the other distribution's moments.