## Abstract

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.

Originalsprache | Englisch |
---|---|

Aufsatznummer | 085702 |

Fachzeitschrift | Journal of Physics A: Mathematical and Theoretical |

Jahrgang | 57 |

Ausgabenummer | 8 |

DOIs | |

Publikationsstatus | Veröffentlicht - 23 Feb. 2024 |