2024/01/17 by Seungjae Lee, Lee, Seungjae, Yeonsu Jeong +5
Computer Science · #Adaptation and Self-Organizing Systems (nlin.AO) #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Dynamics and Pattern Formation #Statistical Mechanics (cond-mat.stat-mech)
paper · pdf · doi:10.48550/arxiv.2401.09081
openalex publication_date 2024/01/17 · openalex created_date 2024/01/19 · openalex updated_date 2026/07/28
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 4D 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.