Multiple Self-Locking in the Kuramoto-Sakaguchi System with Delay

M. Wolfrum*, S. Yanchuk, O. D'Huys

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

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Abstract

We study the Kuramoto-Sakaguchi system of phase oscillators with a delayed mean-field coupling. By applying the theory of large delay to the corresponding Ott-Antonsen equation, we explain fully analytically the mechanisms for the appearance of multiple coexisting partially locked states. Closely above the onset of synchronization, these states emerge in the Eckhaus scenario: With increasing coupling, more and more partially locked states appear unstable from the incoherent state and gain stability for larger coupling at a modulational stability boundary. The partially locked states with strongly detuned frequencies are shown to emerge subcritical and gain stability only after a fold and a series of Hopf bifurcations. We also discuss the role of the Sakaguchi phase lag parameter. For small delays, it determines, together with the delay time, the attraction or repulsion to the central frequency, which leads to supercritical or subcritical behavior, respectively. For large delay, the Sakaguchi parameter does not influence the global dynamical scenario.
Original languageEnglish
Pages (from-to)1709-1725
Number of pages17
JournalSiam Journal on Applied Dynamical Systems
Volume21
Issue number3
DOIs
Publication statusPublished - 2022

Keywords

  • synchronization
  • large delay
  • modulational instability
  • COUPLED OSCILLATORS
  • MODEL
  • BIFURCATIONS
  • SPECTRUM

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