Related papers: Simulating the phase behavior of the Kuramoto tree
We study a simple one-dimensional model of swarmalators, a generalization of phase oscillators that swarm around in space as well as synchronize internal oscillations in time. Previous studies of the model focused on Kuramoto-type…
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…
The Kuramoto model describes the synchronization of coupled oscillators that have different natural frequencies. Among the many generalizations of the original model, Kuramoto and Sakaguchi (KS) proposed a {\it frustrated} version that…
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…
This paper presents a nonlinear control framework for steering networks of coupled oscillators toward desired phase-locked configurations. Inspired by brain dynamics, where structured phase differences support cognitive functions, the focus…
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…
An interesting problem in synchronization is the study of coupled oscillators, wherein oscillators with different natural frequencies synchronize to a common frequency and equilibrium phase difference. In this paper, we investigate the…
Networks of coupled dynamical units give rise to collective dynamics such as the synchronization of oscillators or neurons in the brain. The ability of the network to adapt coupling strengths between units in accordance with their activity…
We solve a longstanding stability problem for the Kuramoto model of coupled oscillators. This system has attracted mathematical attention, in part because of its applications in fields ranging from neuroscience to condensed-matter physics,…
We investigate the role of inertia in the asynchronous state of a disordered Kuramoto model. We extend an iterative simulation scheme to the case of the Kuramoto model with inertia in order to determine the self-consistent fluctuation…
Synchronization of non-identical oscillators coupled through complex networks is an important example of collective behavior. It is interesting to ask how the structural organization of network interactions influences this process. Several…
Models of coupled oscillator networks play an important role in describing collective synchronization dynamics in biological and technological systems. The Kuramoto model describes oscillator's phase evolution and explains the transition…
This paper presents the notion of stochastic phase-cohesiveness based on the concept of recurrent Markov chains and studies the conditions under which a discrete-time stochastic Kuramoto model is phase-cohesive. It is assumed that the…
The behavior of weakly coupled self-sustained oscillators can often be well described by phase equations. Here we use the paradigm of Kuramoto phase oscillators which are coupled in a network to calculate first and second order corrections…
Recently, there has been considerable interest in the study of spontaneous synchronization, particularly within the framework of the Kuramoto model. The model comprises oscillators with distributed natural frequencies interacting through a…
We propose a modification of the Kuramoto model to account for the effective change in the coupling constant among the oscillators, as suggested by some experiments on Josephson junction, laser arrays and mechanical systems, where the…
A new collective behavior of resonant synchronization is discovered and the ability to retrieve information from brain memory is proposed based on this mechanism. We use modified Kuramoto phase oscillator to simulate the dynamics of a…
Complex networks often possess communities defined based on network connectivity. When dynamics undergo in a network, one can also consider dynamical communities; i.e., a group of nodes displaying a similar dynamical process. We have…
The Kuramoto model (KM) of coupled phase oscillators on scale free graphs is analyzed in this work. The W-random graph model is used to define a convergent family of sparse graphs with power law degree distribution. For the KM on this…
The Kuramoto model is the paradigmatic model to study synchronization in coupled oscillator systems. In its classical formulation, the oscillators move on the unit circle, each characterized by a scalar phase and a natural frequency, by…