Related papers: On the numerical integration of the multidimension…
Kuramoto networks constitute a paradigmatic model for the investigation of collective behavior in networked systems. Despite many advances in recent years, many open questions remain on the solutions for systems composed of coupled Kuramoto…
We investigate the dynamics of phase oscillators in the fully disordered Kuramoto model with couplings of defined asymmetry. The mean-field dynamics is reduced to a self-consistent stochastic single-oscillator problem which we analyze…
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…
Orientation-rich images, such as fingerprints and textures, often exhibit coherent angular directional patterns that are challenging to model using standard generative approaches based on isotropic Euclidean diffusion. Motivated by the role…
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 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 $l$.…
Networks of coupled nonlinear oscillators are emerging as powerful physical platforms for implementing Ising machines. Yet the relationship between parametric-oscillator implementations and traditional oscillator-based Ising machines…
We present a generalization of the Kuramoto phase oscillator model in which phases advance in discrete phase increments through Poisson processes, rendering both intrinsic oscillations and coupling inherently stochastic. We study the…
The Kuramoto model describes the collective dynamics of a system of coupled oscillators. An alpha-Kuramoto partition is a graph partition induced by the Kuramoto model, when the oscillators include a phase frustration parameter. We prove…
A common problem in physics and engineering is determination of the orientation of an object given its angular velocity. When the direction of the angular velocity changes in time, this is a nontrivial problem involving coupled differential…
Synchronization of coupled oscillators is often described using the Kuramoto model. Here we study a generalization of the Kuramoto model where oscillators communicate with each other through an external medium. This generalized model…
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…
The numerical integration of the Schr\"odinger equation by discretization of time is explored for the curved manifolds arising from finite representations based on evolving basis states. In particular, the unitarity of the evolution is…
Differential equations are derived which show how generalized Euler vector representations of the Euler rotation axis and angle for a rigid body evolve in time; the Euler vector is also known as a rotation vector or axis-angle vector. The…
Globally coupled phase oscillator models, such as the Kuramoto model, exhibit spontaneous collective synchronization. Such models can be restated in terms of interactions within and between subsets of oscillators. An approximation for the…
Dynamic systems have a fundamental relevance in the description of physical phenomena. The search for more accurate and faster numerical integration methods for the resolution of such systems is, therefore, an important topic of research.…
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…
Due to its description of a synchronization between oscillators, the Kuramoto model is an ideal choice for a synchronisation algorithm in networked systems. This requires to achieve not only a frequency synchronization but also a phase…
We study a nonlinear partial differential equation that arises when introducing inertial effects in the Kuramoto model. Based on the known theory of degenerate Kolmogorov operators, we prove existence, uniqueness and a priori estimates of…
The Kuramoto model has provided deep insights into synchronization phenomena and remains an important paradigm to study the dynamics of coupled oscillators. Yet, despite its success, the asynchronous regime in the Kuramoto model has…