Article ; Online: Relaxation dynamics of phase oscillators with generic heterogeneous coupling.
2023 Volume 107, Issue 2-1, Page(s) 24206
Abstract: The coupled phase oscillator model serves as a paradigm that has been successfully used to shed light on the collective dynamics occurring in large ensembles of interacting units. It was widely known that the system experiences a continuous (second-order) ...
| Abstract | The coupled phase oscillator model serves as a paradigm that has been successfully used to shed light on the collective dynamics occurring in large ensembles of interacting units. It was widely known that the system experiences a continuous (second-order) phase transition to synchronization by gradually increasing the homogeneous coupling among the oscillators. As the interest in exploring synchronized dynamics continues to grow, the heterogeneous patterns between phase oscillators have received ample attention during the past years. Here, we consider a variant of the Kuramoto model with quenched disorder in their natural frequencies and coupling. Correlating these two types of heterogeneity via a generic weighted function, we systematically investigate the impacts of the heterogeneous strategies, the correlation function, and the natural frequency distribution on the emergent dynamics. Importantly, we develop an analytical treatment for capturing the essential dynamical properties of the equilibrium states. In particular, we uncover that the critical threshold corresponding to the onset of synchronization is unaffected by the location of the inhomogeneity, which, however, does depend crucially on the value of the correlation function at its center. Furthermore, we reveal that the relaxation dynamics of the incoherent state featuring the responses to external perturbations is significantly shaped by all the considered effects, thereby leading to various decaying mechanisms of the order parameters in the subcritical region. Moreover, we untangle that synchronization is facilitated by the out-coupling strategy in the supercritical region. Our study is a step forward in highlighting the potential importance of the inhomogeneous patterns involved in the complex systems, and could thus provide theoretical insights for profoundly understanding the generic statistical mechanical properties of the steady states toward synchronization. |
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| Language | English |
| Publishing date | 2023-03-17 |
| Publishing country | United States |
| Document type | Journal Article |
| ZDB-ID | 2844562-4 |
| ISSN | 2470-0053 ; 2470-0045 |
| ISSN (online) | 2470-0053 |
| ISSN | 2470-0045 |
| DOI | 10.1103/PhysRevE.107.024206 |
| Database | MEDical Literature Analysis and Retrieval System OnLINE |
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