Phase Transitions and Chaos in Long-Range Models of Coupled Oscillators

Details Phase Transitions and Chaos in Long-Range Models of Coupled Oscillators Phase Transitions and Chaos in Long-Range Models of Coupled Oscillators

2008-07-11

arxiv.org/abs/0807.1870v4

Europhys.Lett.85:10007,2009

Physics

Condensed Matter

Statistical Mechanics

6 pages, 6 figures. Fig.2,3,5 corrected for the Lyapunov exponents of the Kuramoto model, minor changes in the text

Scientific paper

10.1209/0295-5075/85/10007

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.

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