Cyclops states in repulsive Kuramoto networks: the role of higher-order coupling

Abstract

Repulsive oscillator networks can exhibit multiple cooperative rhythms, including chimera and cluster splay states. Yet, understanding which rhythm prevails remains challenging. Here, we address this fundamental question in the context of Kuramoto-Sakaguchi networks of identical rotators with higher-order coupling. Through analysis and numerics, we show that three-cluster splay states with two distinct coherent clusters and a solitary oscillator are the prevalent rhythms in networks with an odd number of units. We denote such tripod patterns cyclops states with the solitary oscillator reminiscent of the Cyclops's eye. As their mythological counterparts, the cyclops states are giants that dominate the system's phase space in weakly repulsive networks with first-order coupling. Astonishingly, the addition of the second or third harmonics to the Kuramoto coupling function makes the cyclops states global attractors practically across the full range of coupling's repulsion. At a more general level, our results suggest clues for finding dominant rhythms in repulsive physical and biological networks.

References in corpus (14)

• Low Dimensional Behavior of Large Systems of Globally Coupled Oscillators
• Chimera states: Coexistence of coherence and incoherence in networks of coupled oscillators
• Explosive Synchronization Transitions in Scale-free Networks
• Exact Results for the Kuramoto Model with a Bimodal Frequency Distribution
• Partially integrable dynamics of hierarchical populations of coupled oscillators
• Synchronization in networks of networks: the onset of coherent collective behavior in systems of interacting populations of heterogeneous oscillators
• Instability of synchronized motion in nonlocally coupled neural oscillators
• Symmetric States Requiring System Asymmetry
• Entrainment transition in populations of random frequency oscillators
• The smallest chimera states
• Disorder induces explosive synchronization
• Low-dimensional behavior of Kuramoto model with inertia in complex networks
• Generalized splay states in phase oscillator networks
• Stability of rotatory solitary states in Kuramoto networks with inertia

Cited by in corpus (4)

• Synchronization transitions in Kuramoto networks with higher-mode interaction
• Dynamics of large oscillator populations with random interactions
• Resonant Solitary States in Complex Networks
• Kinetic description of one-dimensional stochastic dynamics with small inertia