Related papers: Dynamical equivalence between Kuramoto models with…
Coupled oscillator networks provide mathematical models for interacting periodic processes. If the coupling is weak, phase reduction -- the reduction of the dynamics onto an invariant torus -- captures the emergence of collective dynamical…
Models of coupled oscillators are used to describe a wide variety of phenomena in neuroimaging. These models typically rest on the premise that oscillator dynamics do not evolve beyond their respective limit cycles, and hence that…
We have studied the dynamics of the paradigmatic Kuramoto-Sakaguchi model of identical coupled phase oscilla- tors with various kinds of time-dependent connectivity using Eulerian discretization. We first explore the parameter spaces for…
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,…
We introduce a generalization of the Kuramoto model by explicit consideration of time-dependent parameters. The oscillators' natural frequencies and/or couplings are supposed to be influenced by external, time-dependant fields, with…
The Kuramoto model, describing the synchronization dynamics of coupled oscillators, has been generalized in many ways over the past years. One recent extension of the model replaces the oscillators, originally characterized by a single…
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…
Networks in nature have complex interactions among agents. One significant phenomenon induced by interactions is synchronization of coupled agents, and the interactive network topology can be tuned to optimize synchronization. The previous…
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…
We consider a finite number of coupled oscillators as an adaptation of the Kuramoto model of populations of oscillators. The synchronized solutions are characterized by an integer $m$, the winding number, and a second integer $l$.…
Various macroscopic oscillations, such as the heartbeat and the flashing of fireflies, are created by synchronizing oscillatory units (oscillators). To elucidate the mechanism of synchronization, several coupled oscillator models have been…
A system of nearest neighbors Kuramoto-like coupled oscillators placed in a ring is studied above the critical synchronization transition. We find a richness of solutions when the coupling increases, which exists only within a solvability…
The cluster synchronization (CS) is a very important characteristic for the higher harmonic cou- pling Kuramoto system. A novel method from the symmetry transformation is provided, and it gives CS a profoundly mathematical explanation and…
We explore the collective phase dynamics of Wien-bridge oscillators coupled resistively. We carefully analyze the behavior of two coupled oscillators, obtaining a transformation from voltage to effective phase. From the phase dynamics we…
Artificial neural networks and their applications in deep learning have recently made an incursion into the field of control. Deep learning techniques in control are often related to optimal control, which relies on Pontryagin maximum…
As exemplified by the Kuramoto model, large systems of coupled oscillators may undergo a transition to phase coherence with increasing coupling strength. It is shown that below the critical coupling strength for this transition such systems…
It is shown that, in the infinite size limit, certain systems of globally coupled phase oscillators display low dimensional dynamics. In particular, we derive an explicit finite set of nonlinear ordinary differential equations for the…
Synchronization commonly occurs in many natural and man-made systems, from neurons in the brain to cardiac cells to power grids to Josephson junction arrays. Transitions to or out of synchrony for coupled oscillators depend on several…
The Kuramoto-Sakaguchi model for coupled phase oscillators with phase-frustration is often studied in the thermodynamic limit of infinitely many oscillators. Here we extend a model reduction method based on collective coordinates to capture…
We study synchronization properties of coupled oscillators on networks that allow description in terms of global mean field coupling. These models generalize the standard Kuramoto-Sakaguchi model, allowing for different contributions of…