Related papers: The stability of fixed points for a Kuramoto model…
We study dynamics of phase-differences (PDs) of coupled oscillators where both the intrinsic frequencies and the couplings vary in time. In case the coupling coefficients are all nonnegative, we prove that the PDs are asymptotically stable…
We study the phase diagram and the stability of the ground state for certain four-dimensional gauge-Yukawa theories whose high-energy behaviour is controlled by an interacting fixed point. We also provide analytical and numerical results…
This study examines the Kuramoto model with a Hebbian learning rule and second-order Fourier coupling for binary pattern recognition. The system stores memorized binary patterns as stable critical points, enabling it to identify the closest…
We study the finite-size Kuramoto model of all-to-all coupled phase oscillators with heterogeneous natural frequencies and characterize the minimal coupling strength required for the existence of a fully phase-locked equilibrium (in a…
Beginning with the work of Lohe [14,15] there have been a number of papers [3,5,8,9,11] that have generalized the Kuramoto model for phase-locking to a non-commuting situation. Here we propose and analyze another such model. We consider a…
We consider the Kuramoto model of an ensemble of interacting oscillators allowing for an arbitrary distribution of frequencies and coupling strengths. We define a family of traveling wave states as stationary in a rotating frame, and derive…
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…
We investigate the infra-red stability of the fixed points in the evolution of the Yukawa couplings, $A$-parameters and soft scalar masses in a broad class of supersymmetric theories. We show that the issue of stability is essentially…
The recently introduced continuous Hopfield network (see Ramsauer et al.) exhibits large memorization capabilities, which manifest as attractive fixed points of its update rule -- a differentiable function consisting of two linear mappings…
Kuramoto model is one of the most prominent models for the synchronization of coupled oscillators. It has long been a research hotspot to understand how natural frequencies, the interaction between oscillators, and network topology…
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…
The Kuramoto model provides a concrete mathematical realization of emergent synchrony in a population of phase-coupled oscillators. Since Kuramoto's publication, \textit{Oscillations, Waves, and Turbulence}, researchers have worked to…
Motivated by recent interest for multi-agent systems and smart power grid architectures, we discuss the synchronization problem for the network-reduced model of a power system with non-trivial transfer conductances. Our key insight is to…
The problem of controlling and stabilising solutions to the Kuramoto-Sivashinsky equation is studied in this paper. We consider a generalised form of the equation in which the effects of an electric field and dispersion are included. Both…
Partial integrability in phase-oscillator dynamics is typically examined for identically connected oscillators or groups thereof. Yet, the precise connectivity conditions that ensure conserved quantities on general networks remain unclear.…
Real world systems comprised of coupled oscillators have the ability to exhibit spontaneous synchronization and other complex behaviors. The interplay between the underlying network topology and the emergent dynamics remains a rich area of…
In his classical work, Kuramoto analytically described the onset of synchronization in all-to-all coupled networks of phase oscillators with random intrinsic frequencies. Specifically, he identified a critical value of the coupling…
The Kuramoto model (KM) of coupled phase oscillators on complete, Paley, and Erdos-Renyi (ER) graphs is analyzed in this work. As quasirandom graphs, the complete, Paley, and ER graphs share many structural properties. For instance, they…
Determining the number of stable phase-locked solutions for locally coupled Kuramoto models is a long-standing mathematical problem with important implications in biology, condensed matter physics and electrical engineering among others. We…
Synchronization of an ensemble of oscillators is an emergent phenomenon present in several complex systems, ranging from social and physical to biological and technological systems. The most successful approach to describe how coherent…