Landau damping effects in the synchronization of conformist and contrarian oscillators

TL;DR

This paper demonstrates that Landau damping-like effects are common in the synchronization of phase oscillators with conformist and contrarian populations, revealing new insights into stability and critical coupling.

Contribution

It provides an analytical solution for the stability of incoherent states in mixed conformist-contrarian oscillator systems, extending understanding of collective synchronization phenomena.

Findings

Landau damping effects are prevalent in oscillator synchronization.

Critical coupling strength for stability is analytically determined.

Numerical simulations confirm theoretical predictions.

Abstract

Two decades ago, a phenomenon resembling Landau damping was described in the synchronization of globally coupled oscillators: the evidence of a regime where the order parameter decays when linear theory predicts neutral stability for the incoherent state. We here show that such an effect is far more generic, as soon as phase oscillators couple to their mean field according to their natural frequencies, being then grouped into two distinct populations of conformists and contrarians. We report the analytical solution of this latter situation, which allows determining the critical coupling strength and the stability of the incoherent state, together with extensive numerical simulations that fully support all theoretical predictions. The relevance of our results is discussed in relationship to collective phenomena occurring in polarized social systems.