Heterogeneity induces cyclops states in Kuramoto networks with higher-mode coupling.

Abstract

Disorder is often seen as detrimental to collective dynamics, yet recent work has shown that heterogeneity can enhance network synchronization. However, its constructive role in stabilizing nontrivial cooperative patterns remains largely unexplored. In this Letter, we show that frequency heterogeneity among oscillators can induce stable cyclops and cluster states in Kuramoto networks with higher-mode coupling, even though these states are unstable in the identical oscillator case. Cyclops states, introduced in [Munyaev et al., Phys. Rev. Lett. 130, 107201 (2023)0031-900710.1103/PhysRevLett.130.107201], feature two synchronized clusters and a solitary oscillator, requiring a delicate phase balance. Surprisingly, heterogeneity alone is sufficient to stabilize these patterns across a sizable range of detuning values without needing to be compensated by other forms of disorder or external tuning. To explain this effect, we introduce a mesoscopic collective coordinate approach that links microscopic frequency structure with mean-field cluster-level stability. Importantly, we demonstrate that the same disorder-induced stabilization mechanism also arises robustly in biologically and physically grounded networks of Winfree and Stuart-Landau oscillators, pointing to its generality and opening directions for designing multistate dynamics in heterogeneous networks.