Bifurcations in the Time-Delayed Kuramoto Model of Coupled Oscillators: Exact Results
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DOI: 10.1007/s10955-019-02299-z
Abstract: In the context of the Kuramoto model of coupled oscillators with distributed natural frequencies interacting through a time-delayed mean-field, we derive as a function of the delay exact results for the stability boundary between the… read more here.
Keywords: coupled oscillators; kuramoto model; exact results; time delayed ... See more keywords
A Matrix-Valued Kuramoto Model
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DOI: 10.1007/s10955-019-02442-w
Abstract: The Kuramoto model is an important model for studying the onset of phase-locking in an ensemble of nonlinearly coupled phase oscillators. Each oscillator has a natural frequency (often taken to be random) and interacts with… read more here.
Keywords: kuramoto model; model; phase locked; matrix valued ... See more keywords
Phase transition and scaling in Kuramoto model with high-order coupling
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DOI: 10.1007/s11071-021-06268-8
Abstract: The classical Kuramoto model serves as a useful tool for studying synchronization transitions in coupled oscillators that is limited to the sinusoidal and pairwise interactions. In this paper, we extend the classical Kuramoto model to… read more here.
Keywords: phase transition; order; kuramoto model; high order ... See more keywords
Synchronization in a Kuramoto model with delay-dependent couplings
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DOI: 10.1063/1.5044497
Abstract: This paper aims to provide bifurcation analysis for a Kuramoto model with time-delay and random coupling strength. A delay differential equation governing the system is obtained on the Ott-Antonsen’s manifold, and the bifurcation analysis is… read more here.
Keywords: kuramoto model; delay; bifurcation; distribution ... See more keywords
Synchronization transition in Sakaguchi-Kuramoto model on complex networks with partial degree-frequency correlation.
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DOI: 10.1063/1.5045836
Abstract: We investigate transition to synchronization in the Sakaguchi-Kuramoto (SK) model on complex networks analytically as well as numerically. Natural frequencies of a percentage (f) of higher degree nodes of the network are assumed to be… read more here.
Keywords: kuramoto model; transition; sakaguchi kuramoto; degree frequency ... See more keywords
Clustering and Bellerophon state in Kuramoto model with second-order coupling.
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DOI: 10.1063/1.5085407
Abstract: In this paper, clustering in the Kuramoto model with second-order coupling is investigated under the bimodal Lorentzian frequency distribution. By linear stability analysis and the Ott-Antonsen ansatz treatment, the critical coupling strength for the synchronization… read more here.
Keywords: order; kuramoto model; second order; model second ... See more keywords
Dynamical equivalence between Kuramoto models with first- and higher-order coupling.
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DOI: 10.1063/1.5118941
Abstract: The Kuramoto model with high-order coupling has recently attracted some attention in the field of coupled oscillators in order, for instance, to describe clustering phenomena in sets of coupled agents. Instead of considering interactions given… read more here.
Keywords: order; kuramoto model; higher order; order coupling ... See more keywords
Synchronization transition in the two-dimensional Kuramoto model with dichotomous noise.
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DOI: 10.1063/5.0056001
Abstract: We numerically study the celebrated Kuramoto model of identical oscillators arranged on the sites of a two-dimensional periodic square lattice and subject to nearest-neighbor interactions and dichotomous noise. In the nonequilibrium stationary state attained after… read more here.
Keywords: kuramoto model; transition; time; two dimensional ... See more keywords
The Kuramoto model on a sphere: Explaining its low-dimensional dynamics with group theory and hyperbolic geometry.
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DOI: 10.1063/5.0060233
Abstract: We study a system of N identical interacting particles moving on the unit sphere in d-dimensional space. The particles are self-propelled and coupled all to all, and their motion is heavily overdamped. For d=2, the… read more here.
Keywords: kuramoto model; low dimensional; model; geometry ... See more keywords
Continuum limit of the adaptive Kuramoto model.
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DOI: 10.1063/5.0226759
Abstract: We investigate the dynamics of the adaptive Kuramoto model with slow adaptation in the continuum limit, N→∞. This model is distinguished by dense multistability, where multiple states coexist for the same system parameters. The underlying… read more here.
Keywords: kuramoto model; continuum limit; model; adaptive kuramoto ... See more keywords
Binary system modes of matrix-coupled multidimensional oscillators
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DOI: 10.1088/1367-2630/ad4e5a
Abstract: The standard Kuramoto model has been instrumental in explaining synchronization and desynchronization, two emergent phenomena often observed in biological, neuronal, and physical systems. While the Kuramoto model has turned out effective with one-dimensional oscillators, real-world… read more here.
Keywords: system modes; matrix coupled; kuramoto model; model ... See more keywords