Shear diversity prevents collective synchronization

TL;DR

This paper demonstrates that in ensembles of oscillators with distributed shear, collective synchronization cannot occur if shear diversity exceeds a specific threshold, challenging previous assumptions about synchronization mechanisms.

Contribution

The authors provide the first analytical results for the Kuramoto model incorporating distributed shear, revealing a fundamental limit to synchronization due to shear diversity.

Findings

Synchronization is impossible if shear distribution width exceeds a threshold.

Shear diversity cannot be offset by diffusive coupling.

Analytical conditions for the onset of synchronization are derived.

Abstract

Large ensembles of heterogeneous oscillators often exhibit collective synchronization as a result of mutual interactions. If the oscillators have distributed natural frequencies and common shear (or nonisochronicity), the transition from incoherence to collective synchronization is known to occur at large enough values of the coupling strength. However, here we demonstrate that shear diversity cannot be counterbalanced by diffusive coupling leading to synchronization. We present the first analytical results for the Kuramoto model with distributed shear, and show that the onset of collective synchronization is impossible if the width of the shear distribution exceeds a precise threshold.