Details

Autor(en) / Beteiligte

• Munyayev, Vyacheslav O
• Bolotov, Maxim I
• Smirnov, Lev A
• Osipov, Grigory V
• Belykh, Igor

Titel

Cyclops States in Repulsive Kuramoto Networks: The Role of Higher-Order Coupling

Ist Teil von

• Physical review letters, 2023-03, Vol.130 (10), p.107201-107201, Article 107201

Ort / Verlag

United States

Erscheinungsjahr

2023

Quelle

American Physical Society

Beschreibungen/Notizen

• 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 rotators with higher-order Fourier modes in the 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' 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. Beyond the Kuramoto oscillators, we show that this effect is robustly present in networks of canonical theta neurons with adaptive coupling. At a more general level, our results suggest clues for finding dominant rhythms in repulsive physical and biological networks.