Related papers: Extracting phase coupling functions between collec…
We study a Kuramoto-like model of coupled identical phase oscillators on a network, where attractive and repulsive couplings are balanced dynamically due to nonlinearity in interaction. Under a week force, an oscillator tends to follow the…
We investigate two recently proposed multivariate time series analysis techniques that aim at detecting phase synchronization clusters in spatially extended, nonstationary systems with regard to field applications. The starting point of…
This work introduces a methodology for studying synchronization in adaptive networks with heterogeneous plasticity (adaptation) rules. As a paradigmatic model, we consider a network of adaptively coupled phase oscillators with…
We study synchronization of sinusoidally coupled phase oscillators on networks with modular structure and a large number of oscillators in each community. Of particular interest is the hierarchy of local and global synchrony, i.e.,…
The study of synchronization in populations of coupled biological oscillators is fundamental to many areas of biology to include neuroscience, cardiac dynamics and circadian rhythms. Studying these systems may involve tracking the…
In dynamical systems on networks, one assigns the dynamics to nodes, which are then coupled via links. This approach does not account for group interactions and dynamics on links and other higher dimensional structures. Higher-order network…
We report the observation of a novel and non-trivial synchronization state in a system consisting of three oscillators coupled in a linear chain. For certain ranges of coupling strength the weakly coupled oscillator pair exhibits phase…
A novel regime of synchronization, called remote synchronization, where the peripheral nodes form a phase synchronized cluster not including the hub, was recently observed in star motifs. We show the existence of a more general dynamical…
By spreading phases on the unit circle, desynchronization algorithm is a powerful tool to achieve round-robin scheduling, which is crucial in applications as diverse as media access control of communication networks, realization of…
Time series datasets often contain heterogeneous signals, composed of both continuously changing quantities and discretely occurring events. The coupling between these measurements may provide insights into key underlying mechanisms of the…
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…
We construct an analytical theory of interplay between synchronizing effects by common noise and by global coupling for a general class of smooth limit-cycle oscillators. Both the cases of attractive and repulsive coupling are considered.…
This paper establishes a global contraction property for networks of phase-coupled oscillators characterized by a monotone coupling function. The contraction measure is a total variation distance. The contraction property determines the…
We study a network of 500 coupled modified van der Pol oscillators. The value of a parameter associated with each oscillator is drawn from a normal distribution, giving a heterogeneous network. For strong enough coupling the oscillators all…
In systems of coupled oscillators, the effects of complex signaling can be captured by time delays and phase shifts. Here, we show how time delays and phase shifts lead to different oscillator dynamics and how synchronization rates can be…
There are three key factors of a system of coupled oscillators that characterize the interaction among them: coupling (how to affect), delay (when to affect) and topology (whom to affect). For each of them, the existing work has mainly…
In this paper, we study pairs of oscillators that are indirectly coupled via active (excitable) cells. We introduce a scalar phase model for coupled oscillators and excitable cells. We first show that one excitable and one oscillatory cell…
This paper introduces coordinate-independent methods for analysing multiscale dynamical systems using numerical techniques based on the transfer operator and its adjoint. In particular, we present a method for testing whether an arbitrary…
The onset of collective behavior in a population of globally coupled oscillators with randomly distributed frequencies is studied for phase dynamical models with arbitrary coupling; the effect of a stochastic temporal variation in the…
Constructing generative models for functional observations is an important task in statistical functional analysis. In general, functional data contains both phase (or x or horizontal) and amplitude (or y or vertical) variability. Tradi-…