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We generalize the Kuramoto model for coupled phase oscillators by allowing the frequencies to drift in time according to Ornstein-Uhlenbeck dynamics. Such drifting frequencies were recently measured in cellular populations of circadian…
We analyze the properties of order parameters measuring synchronization and phase locking in complex oscillator networks. First, we review network order parameters previously introduced and reveal several shortcomings: none of the…
We propose new mathematical optimization models for generating sparse dynamical graphs, or networks, that can achieve synchronization. The synchronization phenomenon is studied using the Kuramoto model, defined in terms of the adjacency…
Networks of coupled nonlinear oscillators are emerging as powerful physical platforms for implementing Ising machines. Yet the relationship between parametric-oscillator implementations and traditional oscillator-based Ising machines…
We analyze star-type networks of phase oscillators by virtue of two methods. For identical oscillators we adopt the Watanabe-Strogatz approach, that gives full an- alytical description of states, rotating with constant frequency. For…
We introduce and investigate the effects of a new class of stochastic resetting protocol called subsystem resetting, whereby a subset of the system constituents in a many-body interacting system undergoes bare evolution interspersed with…
In this numerical work we have systematically studied the dynamical phase transitions in the Kuramoto- Sakaguchi model of synchronizing phase oscillators controlled by disorder in the Sakaguchi phases. We find out the numerical steady state…
We study the synchronisation properties of the Kuramoto model of coupled phase oscillators on a general network. Here we distinguish the ability of such a system to self-synchronise from the stability of this behaviour. While…
We perform a stochastic model reduction of the Kuramoto-Sakaguchi model for finitely many coupled phase oscillators with phase frustration. Whereas in the thermodynamic limit coupled oscillators exhibit stationary states and a constant…
We present a rigorous mathematical framework establishing the equivalence of four classical notions of synchronization full phase-locking, phase-locking, frequency synchronization, and order parameter synchronization in generalized Kuramoto…
Large networks of coupled oscillators appear in many branches of science, so that the kinds of phenomena they exhibit are not only of intrinsic interest but also of very wide importance. In 1975, Kuramoto proposed an analytically tractable…
The self-consistent method, first introduced by Kuramoto, is a powerful tool for the analysis of the steady states of coupled oscillator networks. For second-order oscillator networks complications to the application of the self-consistent…
We consider the nonlinear extension of the Kuramoto model of globally coupled phase oscillators where the phase shift in the coupling function depends on the order parameter. A bifurcation analysis of the transition from fully synchronous…
The activity of collections of synchronizing neurons can be represented by weakly coupled nonlinear phase oscillators satisfying Kuramoto's equations. In this article, we build such neural-oscillator models, partly based on…
We examine analytically and numerically a variant of the stochastic Kuramoto model for phase oscillators coupled on a general network. Two populations of phased oscillators are considered, labelled `Blue' and `Red', each with their…
Networked systems have been used to model and investigate the dynamical behavior of a variety of systems. For these systems, different levels of complexity can be considered in the modeling procedure. On one hand, this can offer a more…
Now a standard in Nonlinear Sciences, the Kuramoto model is the perfect example of the transition to synchrony in heterogeneous systems of coupled oscillators. While its basic phenomenology has been sketched in early works, the…
Kuramoto oscillators are widely used to explain collective phenomena in networks of coupled oscillatory units. We show that simple networks of two populations with a generic coupling scheme, where both coupling strengths and phase lags…
Solitary states emerge in oscillator networks when one oscillator separates from the fully synchronized cluster and becomes incoherent with the rest of the network. Such chimera-type patterns with an incoherent state formed by a single…
Higher-order interactions fundamentally shape collective dynamics in oscillator networks. The topological Kuramoto model captures these effects by extending synchronization models to include interactions between cells of arbitrary dimension…