Collective dynamics of identical phase oscillators with high-order coupling

TL;DR

This paper investigates the collective behavior of identical phase oscillators with dominant high-order coupling modes, revealing stability conditions, transition parameters, and the potential for neutrally stable chaos through analytical and numerical methods.

Contribution

It introduces a comprehensive framework combining analytical and numerical techniques to analyze high-order coupled oscillators, including stability analysis and chaos conditions.

Findings

Stationary symmetric distribution is neutrally stable in the marginal regime.

Critical parameters for regime transitions are analytically determined.

Neutrally stable chaos can occur under certain conditions.

Abstract

In this paper, we propose a framework to investigate the collective dynamics in ensembles of globally coupled phase oscillators when higher-order modes dominate the coupling. The spatiotemporal properties of the attractors in various regions of parameter space are analyzed. Furthermore, a detailed linear stability analysis proves that the stationary symmetric distribution is only neutrally stable in the marginal regime which stems from the generalized time-reversal symmetry. Moreover, the critical parameters of the transition among various regimes are determined analytically by both the Ott-Antonsen method and linear stability analysis, the transient dynamics are further revealed in terms of the characteristic curves method. Finally, for the more general initial condition the symmetric dynamics could be reduced to a rigorous three-dimensional manifold which shows that the neutrally stable chaos could also occur in this model for particular parameter. Our theoretical analysis and numerical results are consistent with each other, which can help us understand the dynamical properties in general system with higher-order harmonics couplings.