Related papers: Graphop Mean-Field Limits and Synchronization for …
The Kuramoto model is a standard model for the dynamics of coupled oscillator networks. In particular, it is used to study long time behavior such as phase-locking where all oscillators rotate at a common frequency with fixed angle…
We generalize the Kuramoto model of globally coupled oscillators to multifrequency communities. A situation when mean frequencies of two subpopulations are close to resonance 2:1 is considered in detail. We derive uniformly rotating…
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…
The transient stability of power systems and synchronization of non-uniform Kuramoto oscillators are closely related problems. In this paper, we develop a novel regional stability analysis framework based on the proposed region-parametrized…
In this work, we study the synchronization of coupled phase oscillators on the underlying topology of scale-free networks. In particular, we assume that each network's component is an oscillator and that each interacts with the others…
We study the emergence of synchronization in the Kuramoto model on a digraph in the presence of time delays. Assuming the digraph is strongly connected, we first establish a uniform bound on the phase diameter and subsequently prove the…
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…
Networks of phase oscillators can serve as dense associative memories if they incorporate higher-order coupling beyond the classical Kuramoto model's pairwise interactions. Here we introduce a generalized Kuramoto model with combined…
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…
We present a linear stability analysis of the incoherent state in a system of globally coupled, identical phase oscillators subject to colored noise. In that we succeed to bridge the extreme time scales between the formerly studied and…
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…
We investigate the role of the spectral dimension $d_s$ in determining the universality of phase transitions on a complex network. Due to its structural heterogeneity, a complex network generally acts as a disordered system. Specifically,…
This article studies the dynamics of the mean-field approximation of continuous random networks. These networks are stochastic integrodifferential equations driven by Gaussian noise. The kernels in the integral operators are realizations of…
Synchronization in coupled oscillators networks is a remarkable phenomenon of relevance in numerous fields. For Kuramoto oscillators the loss of synchronization is determined by a trade-off between coupling strength and oscillator…
We consider the synchronization of oscillators in complex networks where there is an interplay between the oscillator dynamics and the network topology. Through a remarkable transformation in parameter space and the introduction of virtual…
There are numerous examples of studied real-world systems that can be described as dynamical systems characterized by individual phases and coupled in a network like structure. Within the framework of oscillatory models, much attention has…
Phase reduction is a powerful technique in the study of nonlinear oscillatory systems. Under certain assumptions, it allows us to describe each multidimensional oscillator by a single phase variable, giving rise to simple phase models such…
Nature is pervaded with oscillatory dynamics. In networks of coupled oscillators patterns can arise when the system synchronizes to an external input. Hence, these networks provide processing and memory of input. We present a universal…
We study synchronization in a Kuramoto model of globally coupled phase oscillators with a bi-harmonic coupling function, in the thermodynamic limit of large populations. We develop a method for an analytic solution of self-consistent…
In this paper, we propose a framework to control brain-wide functional connectivity by selectively acting on the brain's structure and parameters. Functional connectivity, which measures the degree of correlation between neural activities…