Stability of the twisted states in a ring of oscillators interacting with distance-dependent delays

• Published in: Physica. D 2024-08, Vol.464, p.134204, Article 134204
• Main Authors: An, Yong-Hyok, Ho, Myong-Su, Kim, Ryong-Son, Choe, Chol-Ung
• Format: Article
• Language: English
• Subjects: Coupled oscillators; Distance-dependent delays; Non-local coupling; Ott–Antonsen reduction; Twisted state
• ISSN: 0167-2789; 1872-8022
• DOI: 10.1016/j.physd.2024.134204

We consider a ring of phase oscillators interacting with distance-dependent time delays in general forms. It is found that the distance-dependent interaction delay is an essential driving mechanism for the twisted state to occur as a generic state. We carry out rigorous stability analysis for the existence and stability of the twisted states along the Ott–Antonsen invariant manifold and derive the exact characteristic equations for the stability conditions for arbitrarily chosen distance-dependent delay function. The complete stability diagrams are illustrated for two types of distance-dependent delay schemes, the propagational and step-wise interaction delays. Our theoretical results are verified using the direct numerical simulations of the model system. •Low-dimensional dynamics of oscillator system with distance-dependent time delays is found along the Ott–Antonsen invariant manifold.•Exact characteristic equations for the stability conditions for arbitrary distance-dependent delays are derived.•Complete stability diagrams are illustrated for two types of distance-dependent delay schemes.