Volcano Transition in a System of Generalized Kuramoto Oscillators with Random Frustrated Interactions
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arXiv
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| Format: | Preprint |
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2024
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| author | Lee, Seungjae Jeong, Yeonsu Son, Seung-Woo Krischer, Katharina |
| author_facet | Lee, Seungjae Jeong, Yeonsu Son, Seung-Woo Krischer, Katharina |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_09081 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Volcano Transition in a System of Generalized Kuramoto Oscillators with Random Frustrated Interactions Lee, Seungjae Jeong, Yeonsu Son, Seung-Woo Krischer, Katharina Adaptation and Self-Organizing Systems Statistical Mechanics Mathematical Physics 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. |
| title | Volcano Transition in a System of Generalized Kuramoto Oscillators with Random Frustrated Interactions |
| topic | Adaptation and Self-Organizing Systems Statistical Mechanics Mathematical Physics |
| url | https://arxiv.org/abs/2401.09081 |