Related papers: A mesoscopic theory for stochastic coupled oscilla…
A family of stochastic processes has quasi-cycle oscillations if the oscillations are sustained by noise. For such a family we define a Kuramoto-type coupling of both phase and amplitude processes. We find that synchronization, as measured…
We consider networks of coupled stochastic oscillators. When coupled we find strong collective oscillations, while each unit remains stochastic. In the limit (N\to \infty) we derive a system of integro-delay equations and show analytically…
The Kuramoto model has been introduced in order to describe synchronization phenomena observed in groups of cells, individuals, circuits, etc... We look at the Kuramoto model with white noise forces: in mathematical terms it is a set of N…
We study a stochastic model of collective motion in which individuals update their orientation through pairwise aligning or anti-aligning copying interactions. We analyze both annealed dynamics, where interaction types are chosen…
We investigate the effect of partial order parameter adaptation in form of general functions on the synchronization behavior of coupled Kuramoto oscillators on top of random hypergraph models. The interactions between the oscillators are…
Kuramoto's differential equation describes a synchronization process between several harmonic oscillators. It has been used to model biological phenomena such as the synchronization of heart cells, the circadian rhythm, or brain waves. It…
Despite being under intense scrutiny for 50 years, the Kuramoto oscillator model has remained a quintessential representative of non-equilibrium phase transitions. One of the reasons for its enduring relevance is the apparent lack of an…
The Kuramoto model and its generalizations have been broadly employed to characterize and mechanistically understand various collective dynamical phenomena, especially the emergence of synchrony among coupled oscillators. Despite almost…
We show that self-consistent partial synchrony in globally coupled oscillatory ensembles is a general phenomenon. We analyze in detail appearance and stability properties of this state in possibly the simplest setup of a biharmonic…
We uncover a solvable generalization of the Kuramoto model in which shears (or nonisochronicities) and natural frequencies are distributed and statistically dependent. We show that the strength and sign of this dependence greatly alter…
Imagine a group of oscillators, each endowed with their own rhythm or frequency, be it the ticking of a biological clock, the swing of a pendulum, or the glowing of fireflies. While these individual oscillators may seem independent of one…
The linear response is studied in globally coupled oscillator systems including the Kuramoto model. We develop a linear response theory which can be applied to systems whose coupling functions are generic. Based on the theory, we examine…
Many systems in physics, chemistry and biology exhibit oscillations with a pronounced random component. Such stochastic oscillations can emerge via different mechanisms, for example linear dynamics of a stable focus with fluctuations,…
We present a collective coordinate approach to study the collective behaviour of a finite ensemble of $N$ stochastic Kuramoto oscillators using two degrees of freedom; one describing the shape dynamics of the oscillators and one describing…
Mean-field theories of the glass transition predict a phase transition to a dynamically arrested state, yet no such transition is observed in experiments or simulations of finite-dimensional systems. We resolve this long-standing…
An ensemble of pulse-coupled phase-oscillators is thoroughly analysed in the presence of a mean-field coupling and a dispersion of their natural frequencies. In spite of the analogies with the Kuramoto setup, a much richer scenario is…
Systematic discovery of reduced-order closure models for multi-scale processes remains an important open problem in complex dynamical systems. Even when an effective lower-dimensional representation exists, reduced models are difficult to…
The celebrated Kuramoto model provides an analytically tractable framework to study spontaneous collective synchronization and comprises globally coupled limit-cycle oscillators interacting symmetrically with one another. The…
Low-dimensional behavior of large systems of globally coupled oscillators has been intensively investigated since the introduction of the Ott-Antonsen ansatz. In this report, we generalize the Ott-Antonsen ansatz to second-order Kuramoto…
We explore the impact of global resetting on Kuramoto-type models of coupled limit-cycle oscillators with distributed frequencies both in absence and presence of noise. The dynamics comprises repeated interruption of the bare dynamics at…