Volcano transition in a system of generalized Kuramoto oscillators with random frustrated interactions

Seungjae Lee, Yeonsu Jeong, Seung Woo Son, Katharina Krischer

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4 Scopus citations


In a system of heterogeneous (Abelian) Kuramoto oscillators with random or ‘frustrated’ interactions, transitions from states of incoherence to partial synchronization were observed. These so-called volcano transitions are characterized by a change in the shape of a local field distribution and were discussed in connection with an oscillator glass. In this paper, we consider a different class of oscillators, namely a system of (non-Abelian) SU(2)-Lohe oscillators that can also be defined on the 3-sphere, i.e. an oscillator is generalized to be defined as a unit vector in four-dimensional Euclidean space. We demonstrate that such higher-dimensional Kuramoto models with reciprocal and nonreciprocal random interactions represented by a low-rank matrix exhibit a volcano transition as well. We determine the critical coupling strength at which a volcano-like transition occurs, employing an Ott-Antonsen ansatz. Numerical simulations provide additional validations of our analytical findings and reveal the differences in observable collective dynamics prior to and following the transition. Furthermore, we show that a system of unit 3-vector oscillators on the 2-sphere does not possess a volcano transition.

Original languageEnglish
Article number085702
JournalJournal of Physics A: Mathematical and Theoretical
Issue number8
StatePublished - 23 Feb 2024


  • generalized Kuramoto model
  • random interaction
  • volcano transition


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