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In a system of heterogeneous (Abelian) Kuramoto oscillators with random or`frustrated' interactions, transitions from states of incoherence to partialsynchronization were observed. These so-called volcano transitions arecharacterized by a change in the shape of a local field distribution and werediscussed in connection with an oscillator glass. In this paper, we consider adifferent class of oscillators, namely a system of (non-Abelian) SU(2)-Loheoscillators that can also be defined on the 3-sphere, i.e., an oscillator isgeneralized to be defined as a unit vector in 4D Euclidean space. Wedemonstrate that such higher-dimensional Kuramoto models with reciprocal andnonreciprocal random interactions represented by a low-rank matrix exhibit avolcano transition as well. We determine the critical coupling strength atwhich a volcano-like transition occurs, employing an Ott-Antonsen ansatz.Numerical simulations provide additional validations of our analytical findingsand reveal the differences in observable collective dynamics prior to andfollowing the transition. Furthermore, we show that a system of unit 3-vectoroscillators on the 2-sphere does not possess a volcano transition.

Volcano Transition in a System of Generalized Kuramoto Oscillators with Random Frustrated Interactions