Frequency Heterogeneity can Promote Order yet Undermine Stability in Kuramoto Networks with Higher-Order Interactions

TL;DR

This paper shows that in Kuramoto networks with higher-order interactions, moderate frequency heterogeneity can enhance global order by restructuring attractor landscapes, despite generally destabilizing individual states.

Contribution

It reveals the dual role of frequency heterogeneity in promoting order through basin restructuring while destabilizing linear stability in higher-order oscillator networks.

Findings

Moderate heterogeneity increases the order parameter in strong triadic coupling.

Heterogeneity shifts attractor competition towards more ordered states.

Linear stability of frequency-locked states decreases with heterogeneity.

Abstract

We investigate the interplay between frequency heterogeneity and higher-order triadic interactions in a ring network of Kuramoto oscillators. While both factors individually disrupt ordered states, their combination produces unexpected collective behavior. In the strong triadic coupling regime, moderate frequency heterogeneity substantially increases the global order parameter, with an optimal heterogeneity strength growing approximately linearly with triadic coupling strength. Basin stability analysis reveals that this order-promoting effect arises from a global restructuring of the attractor landscape: frequency heterogeneity shifts the attractor competition in favor of more ordered configurations. Linear stability analysis of frequency-locked twisted states reveals a competing effect: frequency heterogeneity monotonically erodes linear stability and reduces the probability of frequency locking. These two competing mechanisms, basin enlargement and linear destabilization, together account for the non-monotonic dependence of the order parameter on heterogeneity strength. Our results demonstrate that frequency heterogeneity can play a constructive role in oscillator networks with higher-order interactions.