Related papers: Approximate solution to the stochastic Kuramoto mo…
The Kuramoto model is a canonical framework for analyzing phase synchronization, yet its utility is restricted to the vicinity of the oscillator's unperturbed limit cycle. Here, we present a method to construct coupled-oscillator models…
Employing the Kuramoto model as an illustrative example, we show how the use of the mean field approximation can be applied to large networks of phase oscillators with assortativity. We then use the ansatz of Ott and Antonsen [Chaos 19,…
The high-dimensional generalization of the one-dimensional Kuramoto paradigm has been an essential step in bringing about a more faithful depiction of the dynamics of real-world systems. Despite the multi-dimensional nature of the…
An interesting problem in synchronization is the study of coupled oscillators, wherein oscillators with different natural frequencies synchronize to a common frequency and equilibrium phase difference. In this paper, we investigate the…
We study the mean-field limit of the Kuramoto model of globally coupled oscillators. By studying the evolution in Fourier space and understanding the domain of dependence, we show a global stability result. Moreover, we can identify…
In the Kuramoto model, a uniform distribution of the natural frequencies leads to a first-order (i.e., discontinuous) phase transition from incoherence to synchronization, at the critical coupling parameter $K_c$. We obtain the asymptotic…
Due to its description of a synchronization between oscillators, the Kuramoto model is an ideal choice for a synchronisation algorithm in networked systems. This requires to achieve not only a frequency synchronization but also a phase…
The asymptotic scaling behavior of the Kuramoto model with finite populations has been notably elusive, despite comprehensive investigations employing both analytical and numerical methods. In this paper, we explore the Kuramoto model with…
The Kuramoto model is a paradigmatic model of collective synchronization in coupled oscillator systems. Although its mathematical properties have been extensively investigated, exact phase trajectories from arbitrary initial conditions have…
We investigate the emergence of synchronization in the second-order Kuramoto model with adaptive simplicial interactions on a globally connected network. This inertial Kuramoto framework describes systems, where oscillator frequencies…
The Kuramoto model, a paradigmatic framework for studying synchronization, exhibits a transition to collective oscillations only above a critical coupling strength in the thermodynamic limit. However, real-world systems are finite, and…
We study the Kuramoto model for coupled oscillators. For the case of identical natural frequencies, we give a new proof of the complete frequency synchronization for all initial data; extending this result to the continuous version of the…
We report finite size numerical investigations and mean field analysis of a Kuramoto model with inertia for fully coupled and diluted systems. In particular, we examine for a Gaussian distribution of the frequencies the transition from…
We propose an infinite Kuramoto model for a countably infinite set of Kuramoto oscillators and study its emergent dynamics for two classes of network topologies. For a class of symmetric and row(or column)-summable network topology, we show…
Collective synchronization is often summarized by a complex order parameter $R e^{i\Psi}$, implicitly treating the global phase $\Psi$ as a meaningful macroscopic coordinate. Here we ask when $\Psi$ becomes \emph{operationally well-defined}…
By means of numerical integration we investigate the coherent and incoherent phases in a generalized Kuramoto model of phase-coupled oscillators with distance-dependent delay. Preserving the topology of a complete graph, we arrange the…
The mean-field Kuramoto model for synchronization of phase oscillators with an asymmetric bimodal frequency distribution is analyzed. Breaking the reflection symmetry facilitates oscillator synchronization to rotating wave phases. Numerical…
Networks of phase oscillators can serve as dense associative memories if they incorporate higher-order coupling beyond the classical Kuramoto model's pairwise interactions. Here we introduce a generalized Kuramoto model with combined…
The study of synchronization in populations of coupled biological oscillators is fundamental to many areas of biology to include neuroscience, cardiac dynamics and circadian rhythms. Studying these systems may involve tracking the…
We study the synchronization of a generalized Kuramoto system in which the coupling weights are determined by the phase differences between oscillators. We employ the fast-learning regime in a Hebbian-like plasticity rule so that the…