Related papers: Ott-Antonsen ansatz for the D-dimensional Kuramoto…
Understanding how large complex networks achieve synchronization is a problem of fundamental interest, and is typically studied in the asymptotic steady-state regime. In contrast, this study investigates how higher-order interactions affect…
A system's response to external periodic changes can provide crucial information about its dynamical properties. We investigate the synchronization transition, an archetypical example of a dynamic phase transition, in the framework of such…
We demonstrate the application of the circular cumulant approach for thermodynamically large populations of phase elements, where the Ott-Antonsen properties are violated by a multiplicative intrinsic noise. The infinite cumulant equation…
A knot is a circle embedded in the space. Projecting a knot on a plane, we obtain a diagram which is known as the knot diagram. The vertices of the diagram, where the curved lines are crossed, can be considered as sites occupied by…
The Kuramoto model of coupled phase oscillators is often used to describe synchronization phenomena in nature. Some applications, e.g., quantum synchronization and rigid-body attitude synchronization, involve high-dimensional Kuramoto…
Previous results have shown that a large class of complex systems consisting of many interacting heterogeneous phase oscillators exhibit an attracting invariant manifold. This result has enabled reduced analytic system descriptions from…
The Kuramoto model captures various synchronization phenomena in biological and man-made systems of coupled oscillators. It is well-known that there exists a critical coupling strength among the oscillators at which a phase transition from…
Synchronization is an omnipresent collective phenomenon in nature and technology, whose understanding is in particular for real-world systems still elusive. We study the synchronization transition in a phase oscillator system with two…
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 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…
The higher-order interactions of complex systems, such as the brain are captured by their simplicial complex structure and have a significant effect on dynamics. However, the existing dynamical models defined on simplicial complexes make…
Higher order interactions can lead to new equilibrium states and bifurcations in systems of coupled oscillators described by the Kuramoto model. However, even in the simplest case of 3-body interactions there are more than one possible…
Synchronization in a population of oscillators with hyperbolic chaotic phases is studied for two models. One is based on the Kuramoto dynamics of the phase oscillators and on the Bernoulli map applied to these phases. This system possesses…
The Kuramoto model describes a system of globally coupled phase-only oscillators with distributed natural frequencies. The model in the steady state exhibits a phase transition as a function of the coupling strength, between a low-coupling…
The Kuramoto model for an ensemble of coupled oscillators provides a paradigmatic example of non-equilibrium transitions between an incoherent and a synchronized state. Here we analyze populations of almost identical oscillators in…
Synchronization is a ubiquitous phenomenon in nature and we propose its new perspective in ultrafast dynamics in interacting electron systems. In particular, using graphene irradiated by an intense bi-circular pulse laser as a prototypical…
The Kuramoto model has become a paradigm to describe the dynamics of nonlinear oscillator under the influence of external perturbations, both deterministic and stochastic. It is based on the idea to describe the oscillator dynamics by a…
A general stability analysis is presented for the determination of the transition from incoherent to coherent behavior in an ensemble of globally coupled, heterogeneous, continuous-time dynamical systems. The formalism allows for the…
In this paper, we propose a framework to investigate the collective dynamics in ensembles of globally coupled phase oscillators when higher-order modes dominate the coupling. The spatiotemporal properties of the attractors in various…
The present paper introduces a linear reformulation of the Kuramoto model describing a self-synchronizing phase transition in a system of globally coupled oscillators that in general have different characteristic frequencies. The…