Related papers: Dynamics of multifrequency oscillator communities
We consider a system of N phase oscillators having randomly distributed natural frequencies and diagonalizable interactions among the oscillators. We show that in the limit of N going to infinity, all solutions of such a system are…
Randomly coupled phase oscillators may synchronize into disordered patterns of collective motion. We analyze this transition in a large, fully connected Kuramoto model with symmetric but otherwise independent random interactions. Using the…
Many real-world systems of coupled agents exhibit directed interactions, meaning that the influence of an agent on another is not reciprocal. Furthermore, interactions usually do not have identical amplitude and/or sign. To describe…
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…
In this letter we discuss a method for generating synchrony-optimized coupling architectures of Kuramoto oscillators with a heterogeneous distribution of native frequencies. The method allows us to relate the properties of the coupling…
We present an alternative approach to finite-size effects around the synchronization transition in the standard Kuramoto model. Our main focus lies on the conditions under which a collective oscillatory mode is well defined. For this…
An Ott-Antonsen reduced $M$-population of Kuramoto-Sakaguchi oscillators is investigated, focusing on the influence of the phase-lag parameter $\alpha$ on the collective dynamics. For oscillator populations coupled on a ring, we obtained a…
We present a general theory for the onset of coherence in collections of heterogeneous maps interacting via a complex connection network. Our method allows the dynamics of the individual uncoupled systems to be either chaotic or periodic,…
Improving the frequency precision by synchronizing a lattice of oscillators is studied in the phase reduction limit. For the most commonly studied case of purely dissipative phase coupling (the Kuramoto model) I confirm that the frequency…
From biology to social science, the functioning of a wide range of systems is the result of elementary interactions which involve more than two constituents, so that their description has unavoidably to go beyond simple…
The collective dynamics in populations of magnetic spin torque oscillators (STO) is an intensely studied topic in modern magnetism. Here, we show that arrays of STO coupled via dipolar fields can be modeled using a variant of the Kuramoto…
A dynamics of a low-dimensional ensemble consisting of connected in a network five discrete phase oscillators is considered. A two-parameter synchronization picture which appears instead of the Arnold tongues with an increase of the system…
Synchronisation of coupled oscillators is a ubiquitous phenomenon, occurring in topics ranging from biology and physics, to social networks and technology. A fundamental and long-time goal in the study of synchronisation has been to find…
Understanding the mechanisms that govern collective synchronization is a paramount task in nonlinear dynamics. While higher-order (many-body) interactions have recently emerged as a powerful framework for capturing collective behaviors,…
We consider the problem of synchronization of coupled oscillators in a Kuramoto-type model with lossy couplings. Kuramoto models have been used to gain insight on the stability of power networks which are usually nonlinear and involve large…
We consider general properties of groups of interacting oscillators, for which the natural frequencies are not in resonance. Such groups interact via non-oscillating collective variables like the amplitudes of the order parameters defined…
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…
The transition to synchrony in the Kuramoto model of globally coupled phase oscillators with a uniform distribution of natural frequencies is discontinuous. We extend the theory of this transition to the Kuramoto-Sakaguchi model, taking…
Community structure and interaction delays are common features of ensembles of network coupled oscillators, but their combined effect on the emergence of synchronization has not been studied in detail. We study the transitions between…
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…