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

Author:

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

Keyword:

Nonlinear Sciences, Adaptation and Self-Organizing Systems, Adaptation and Self-Organizing Systems (nlin.AO), Statistical Mechanics (cond-mat.stat-mech), Mathematical Physics (math-ph)

journal:

date:

2024-01-17 00:00:00

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 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.

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