Journal
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
Volume 54, Issue 28, Pages -Publisher
IOP Publishing Ltd
DOI: 10.1088/1751-8121/ac019c
Keywords
synchronization; coupled phase oscillators; phase transition
Categories
Funding
- National Natural Science Foundation of China [11905068]
- Scientific Research Funds of Huaqiao University [ZQN-810]
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The study of an extension of the Kuramoto model with higher-order structure reveals several novel dynamical phenomena and proves the stability of multiple multiclusters. By utilizing the partial dimensionality reduction method proposed by Ott-Antonsen, a rigorous analysis of various multi-cluster states is conducted.
The Kuramoto model consisting of large ensembles of globally coupled phase oscillators serves as a paradigm for modelling synchronization and collective behavior in diverse self-sustained systems. As interest in the effects of higher-order interactions, we study an extension of the Kuramoto model with higher-order structure by considering the correlations between frequency and coupling. The resulting model is exactly solvable and several novel dynamical phenomena including clustering, multistability, and abrupt synchronization (desynchronization) transition emerge. We demonstrate that the extensive multiclusters corresponding to different arrangements of oscillator populations on the circle are established in a universal way that are independent of the choices of frequency distributions (heterogeneity of the ensembles). Using the partial dimensionality reduction of the Ott-Antonsen, we present a rigorous analysis of various multi-cluster states by studying their spectrum in the thermodynamic limit. In particular, we prove that a large multiplicity of the synchronous states are asymptotically stable to perturbation in the tangent space, thereby determining an explicit stability condition for their occurrences in the high-dimensional phase space.
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