Related papers: The stability of fixed points for a Kuramoto model…
In dynamical systems, the full stability of fixed point solutions is determined by their basin of attraction. Characterizing the structure of these basins is, in general, a complicated task, especially in high dimensionality. Recent works…
Networks of coupled neural systems represent an important class of models in computational neuroscience. In some applications it is required that equilibrium points in these networks remain stable under parameter variations. Here we present…
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 present and analyze a nonabelian version of the Kuramoto system, which we call the quantum Kuramoto system. We study the stability of several classes of special solutions to this system, and show that for certain connection topologies…
The Kuramoto-Daido model, which describes synchronization phenomena, is a system of ordinary differential equations on $N$-torus defined as coupled harmonic oscillators, whose natural frequencies are drawn from some distribution function.…
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 prove that the Kuramoto model on a graph can contain infinitely many non-equivalent stable equilibria. More precisely, we prove that for every positive integer d there is a connected graph such that the set of stable equilibria contains…
Adaptive Kuramoto models admit a variety of nontrivial phase-locked configurations, including antipodal and rotating-wave states. A central open question is whether the observed persistence of such configurations can be attributed to…
We study the mean-field limit of the Kuramoto model of globally coupled oscillators. By studying the evolution in Fourier space and understanding the domain of dependence, we show a global stability result. Moreover, we can identify…
The Kuramoto model is a standard model for the dynamics of coupled oscillator networks. In particular, it is used to study long time behavior such as phase-locking where all oscillators rotate at a common frequency with fixed angle…
This paper investigates the global stability and the global asymptotic stability independent of the sizes of the delays of linear time-varying Caputo fractional dynamic systems of real fractional order possessing internal point delays. The…
In view of highly decentralized and diversified power generation concepts, in particular with renewable energies such as wind and solar power, the analysis and control of the stability and the synchronization of power networks is an…
The Kuramoto model for an ensemble of coupled oscillators provides a paradigmatic example of non-equilibrium transitions between an incoherent and a synchronized state. Here we analyze populations of almost identical oscillators in…
In his classical work on synchronization, Kuramoto derived the formula for the critical value of the coupling strength corresponding to the transition to synchrony in large ensembles of all-to-all coupled phase oscillators with randomly…
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…
Inspired by the Deffuant and Hegselmann-Krause models of opinion dynamics, we extend the Kuramoto model to account for confidence bounds, i.e., vanishing interactions between pairs of oscillators when their phases differ by more than a…
Many real-world systems of coupled agents exhibit directed interactions, meaning that the influence of an agent on another is not reciprocal. Furthermore, interactions usually do not have identical amplitude and/or sign. To describe…
The Kuramoto model is a dynamical system that models the interaction of coupled oscillators. There has been much work to effectively bound the number of equilibria to the Kuramoto model for a given network. By formulating the Kuramoto…
We consider the (noisy) Kuramoto model, that is a population of N oscillators, or rotators, with mean-field interaction. Each oscillator has its own randomly chosen natural frequency (quenched disorder) and it is stirred by Brownian motion.…
We propose a graphical notation by which certain spectral properties of complex systems can be rewritten concisely and interpreted topologically. Applying this notation to analyze the stability of a class of networks of coupled dynamical…