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

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.

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

References in corpus (5)

• Geometric approach to Hamiltonian dynamics and statistical mechanics
• Thermodynamic limit of the first-order phase transition in the Kuramoto model
• Out-of-equilibrium tricritical point in a system with long-range interactions
• A closer look at the indications of q-generalized Central Limit Theorem behavior in quasi-stationary states of the HMF model
• Metastability in the Hamiltonian Mean Field model and Kuramoto model

Cited by in corpus (18)

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• A power-law distribution of phase-locking intervals does not imply critical interaction
• Thermostatistics in the neighborhood of the $\pi$-mode solution for the Fermi-Pasta-Ulam $\beta$ system: from weak to strong chaos
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• Lyapunov Exponents, Phase Transitions, and Chaos Bound of ModMax AdS Black Holes
• Relaxation dynamics of the Kuramoto model with uniformly distributed natural frequencies
• Finite-size scaling in globally coupled phase oscillators with a general coupling scheme
• Long-term fluctuations in globally coupled phase oscillators with general coupling: Finite size effects
• A Simple Model for Long-Range Interacting Pendula
• Information geometry and synchronization phase transition in Kuramoto model
• Dynamics and Thermodynamics of the mean field d-HMF model out-of-equilibrium