Journal ArticleDOI
First Order Phase Transition Resulting from Finite Inertia in Coupled Oscillator Systems
Reads0
Chats0
TLDR
In this article, the collective behavior of a set of coupled damped driven pendula with finite inertia was analyzed, and it was shown that the synchronization of the oscillators exhibits a first order phase transition synchronization onset, substantially different from the second order transition obtained in the case of no inertia.Abstract:
We analyze the collective behavior of a set of coupled damped driven pendula with finite (large) inertia, and show that the synchronization of the oscillators exhibits a first order phase transition synchronization onset, substantially different from the second order transition obtained in the case of no inertia. There is hysteresis between two macroscopic states, a weakly and a strongly coherent synchronized state, depending on the coupling and the initial state of the oscillators. A self-consistent theory is shown to determine these cooperative phenomena and to predict the observed numerical data in specific examples. [S0031-9007(97)02614-8]read more
Citations
More filters
Journal ArticleDOI
The Kuramoto model: A simple paradigm for synchronization phenomena
TL;DR: In this paper, a review of the Kuramoto model of coupled phase oscillators is presented, with a rigorous mathematical treatment, specific numerical methods, and many variations and extensions of the original model that have appeared in the last few years.
Journal ArticleDOI
Critical phenomena in complex networks
TL;DR: A wide range of critical phenomena in equilibrium and growing networks including the birth of the giant connected component, percolation, $k$-core percolations, phenomena near epidemic thresholds, condensation transitions,critical phenomena in spin models placed on networks, synchronization, and self-organized criticality effects in interacting systems on networks are mentioned.
Journal ArticleDOI
The Kuramoto model in complex networks
Francisco A. Rodrigues,Thomas K. Dm. Peron,Thomas K. Dm. Peron,Peng Ji,Peng Ji,Jürgen Kurths +5 more
TL;DR: In this article, B. Sonnenschein, E.R. dos Santos, P.J. Schultz, C.A. Ha, M.K. Choi and C.P.
Journal ArticleDOI
Analysis of a power grid using a Kuramoto-like model
TL;DR: In this article, the authors show that there is a link between the Kuramoto paradigm and another system of synchronized oscillators, namely an electrical power distribution grid of generators and consumers, and under some necessary approximations a class of Kuramoto-like models, those with bimodal distribution of the frequencies, is most appropriate for the power-grid.
Journal ArticleDOI
On the Critical Coupling for Kuramoto Oscillators
Florian Dörfler,Francesco Bullo +1 more
TL;DR: In this article, the concept of phase cohesiveness is introduced as an analysis tool and performance index for synchronization in the finite-dimensional Kuramoto model and a necessary and sufficient condition on the critical coupling strength to achieve synchronization is presented.