Related papers: Dynamics of multifrequency oscillator communities
We explore chaos in the Kuramoto model with multimodal distributions of the natural frequencies of oscillators and provide a comprehensive description under what conditions chaos occurs. For a natural frequency distribution with $M$ peaks…
The mean field Kuramoto model describing the synchronization of a population of phase oscillators with a bimodal frequency distribution is analyzed (by the method of multiple scales) near regions in its phase diagram corresponding to…
After decades of study, there are only two known mechanisms to induce global synchronization in a population of oscillators: deterministic coupling and common forcing. The inclusion of independent random forcing in these models typically…
Synchronization is a fundamental phenomenon in complex systems, observed across a wide range of natural and engineered contexts. The Kuramoto model provides a foundational framework for understanding synchronization among coupled…
The understanding of synchronization ranging from natural to social systems has driven the interests of scientists from different disciplines. Here, we have investigated the synchronization dynamics of the Kuramoto dynamics departing from…
We study populations of oscillators, all-to-all coupled by means of quenched disordered phase shifts. While there is no traditional synchronization transition with a nonvanishing Kuramoto order parameter, the system demonstrates a specific…
Synchronization is a universal phenomenon found in many non-equilibrium systems. Much recent interest in this area has overlapped with the study of complex networks, where a major focus is determining how a system's connectivity patterns…
We consider oscillator ensembles consisting of subpopulations of identical units, with a general heterogeneous coupling between subpopulations. Using the Watanabe-Strogatz ansatz we reduce the dynamics of the ensemble to a relatively small…
Kuramoto model is one of the most prominent models for the synchronization of coupled oscillators. It has long been a research hotspot to understand how natural frequencies, the interaction between oscillators, and network topology…
Synchronization is observed in many natural systems, with examples ranging from neuronal activation to walking pedestrians. The models proposed by Winfree and Kuramoto stand as the classic frameworks for investigating these phenomena. The…
The emergence of collective synchrony from an incoherent state is a phenomenon essentially described by the Kuramoto model. This canonical model was derived perturbatively, by applying phase reduction to an ensemble of heterogeneous,…
We consider the (noisy) Kuramoto model, that is a population of N oscillators, or rotators, with mean-field interaction. Each oscillator has its own randomly chosen natural frequency (quenched disorder) and it is stirred by Brownian motion.…
Common models of synchronizable oscillatory systems consist of a collection of coupled oscillators governed by a collection of differential equations. The ubiquitous Kuramoto models rely on an {\em a priori} fixed connectivity pattern…
We give evidence that a population of pure contrarians globally coupled D-dimensional Kuramoto oscillators reaches a collective synchronous state when the interplay between the units goes beyond the limit of pairwise interactions. Namely,…
We analyze the simplest model of identical coupled phase oscillators subject to two-body and three-body interactions with permutation symmetry. This model is derived from an ensemble of weakly coupled nonlinear oscillators by phase…
Partial synchronous states appear between full synchrony and asynchrony and exhibit many interesting properties. Most frequently, these states are studied within the framework of phase approximation. The latter is used ubiquitously to…
We study the noisy Kuramoto model for two interacting communities of oscillators, where we allow the interaction in and between communities to be positive or negative (but not zero). We find that, in the thermodynamic limit where the size…
Synchronization of non-identical oscillators coupled through complex networks is an important example of collective behavior. It is interesting to ask how the structural organization of network interactions influences this process. Several…
In the context of the celebrated Kuramoto model of globally-coupled phase oscillators of distributed natural frequencies, which serves as a paradigm to investigate spontaneous collective synchronization in many-body interacting systems, we…
We study the synchronization of a small-world network of identical coupled phase oscillators with Kuramoto interaction. First, we consider the model with instantaneous mutual interaction and the normalized coupling constant to the degree of…