A moment based approach to the dynamical solution of the Kuramoto model

Abstract

We examine the dynamics of the Kuramoto model with a new analytical approach. By defining an appropriate set of moments the dynamical equations can be exactly closed. We discuss some applications of the formalism like the existence of an effective Hamiltonian for the dynamics. We also show how this approach can be used to numerically investigate the dynamical behavior of the model without finite size effects.

6 pages, 5 figures, Revtex file, to appear in J. Phys. A

References in corpus (5)

• Amplitude Expansions for Instabilities in Populations of Globally-Coupled Oscillators
• Scaling and singularities in the entrainment of globally-coupled oscillators
• On Self-Organized Criticality and Synchronization in Lattice Models of Coupled Dynamical Systems
• Glassy Mean-Field Dynamics of the Backgammon model
• Closure of the Monte Carlo dynamical equations in the spherical Sherrington-Kirkpatrick model

Cited by in corpus (13)

• Exactly solvable phase oscillator models with synchronization dynamics
• Asymptotic description of transients and synchronized states of globally coupled oscillators
• Solvable dynamics in a system of interacting random tops
• A global synchronization theorem for oscillators on a random graph
• Structure preserving schemes for the continuum Kuramoto model: phase transitions
• Sufficiently dense Kuramoto networks are globally synchronizing
• Multibranch entrainment and slow evolution among branches in coupled oscillators
• Acceleration effect caused by the Onsager reaction term in a frustrated coupled oscillator system
• Acceleration effect of coupled oscillator systems
• Continuous limit of the moments system for the globally coupled phase oscillators
• Exact solutions and dynamics of globally coupled phase oscillators
• Spatio-temporal patterns of active epigenetic turnover
• Efficient moment-based approach to the simulation of infinitely many heterogeneous phase oscillators