Phase Transitions and Chaos in Long-Range Models of Coupled Oscillators
Statistical Mechanics
2016-09-08 v4 Astrophysics
Chaotic Dynamics
Nuclear Theory
Classical Physics
Plasma Physics
Abstract
We study the chaotic behavior of the synchronization phase transition in the Kuramoto model. We discuss the relationship with analogous features found in the Hamiltonian Mean Field (HMF) model. Our numerical results support the connection between the two models, which can be considered as limiting cases (dissipative and conservative, respectively) of a more general dynamical system of damped-driven coupled pendula. We also show that, in the Kuramoto model, the shape of the phase transition and the largest Lyapunov exponent behavior are strongly dependent on the distribution of the natural frequencies.
Cite
@article{arxiv.0807.1870,
title = {Phase Transitions and Chaos in Long-Range Models of Coupled Oscillators},
author = {G. Miritello and A. Pluchino and A. Rapisarda},
journal= {arXiv preprint arXiv:0807.1870},
year = {2016}
}
Comments
6 pages, 6 figures. Fig.2,3,5 corrected for the Lyapunov exponents of the Kuramoto model, minor changes in the text