Issue
EPL
Volume 85, Number 1, January 2009
Article Number 10007
Number of page(s) 6
Section General
DOI http://dx.doi.org/10.1209/0295-5075/85/10007
Published online 16 January 2009
EPL, 85 (2009) 10007
DOI: 10.1209/0295-5075/85/10007

Phase transitions and chaos in long-range models of coupled oscillators

G. Miritello, A. Pluchino and A. Rapisarda

Dipartimento di Fisica e Astronomia, Università di Catania, and INFN sezione di Catania Via S. Sofia 64, I-95123 Catania, Italy, EU

andrea.rapisarda@ct.infn.it

received 26 July 2008; accepted in final form 4 November 2008; published January 2009
published online 16 January 2009

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.

PACS
05.45.Jn - High-dimensional chaos.
05.45.Xt - Synchronization; coupled oscillators.
05.70.Fh - Phase transitions: general studies.

© EPLA 2009