Asymptotic description of transients and synchronized states of globally coupled oscillators

DOI10.1016/S0167-2789(97)00197-8zbMath0935.34032arXivpatt-sol/9706003MaRDI QIDQ1963432

Juan A. Acebrón, Luis L. Bonilla

Publication date: 1 February 2000

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/patt-sol/9706003

zbMATH Keywords

probability densitytraveling wavesnumerical simulationsbifurcation pointssynchronized statestransientsnonlinear Fokker-Planck equationhigh-frequency limitglobally coupled oscillatorsincoherent solutionsmultimodal mean-field Kuramoto modelreflection-symmetric bimodal frequency distributions

Mathematics Subject Classification ID

Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Ordinary differential equations and systems with randomness (34F05) Asymptotic properties of solutions to ordinary differential equations (34D05) Asymptotic expansions of solutions to ordinary differential equations (34E05) Multiple scale methods for ordinary differential equations (34E13)

Related Items (8)

Interacting universes and the cosmological constant ⋮ Experimental results on synchronization times and stable states in locally coupled light-controlled oscillators ⋮ Bifurcation of the collective oscillatory state in phase oscillators with heterogeneity coupling ⋮ Structure preserving schemes for the continuum Kuramoto model: phase transitions ⋮ Effect of noise on the collective dynamics of a heterogeneous population of active rotators ⋮ Uncertainty in phase-frequency synchronization of large populations of globally coupled nonlinear oscillators ⋮ EXACT SOLUTIONS AND DYNAMICS OF GLOBALLY COUPLED OSCILLATORS ⋮ A proof of the Kuramoto conjecture for a bifurcation structure of the infinite-dimensional Kuramoto model

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Chemical oscillations, waves, and turbulence
• Amplitude response of coupled oscillators
• Phase-locking and critical phenomena in lattices of coupled nonlinear oscillators with random intrinsic frequencies
• Nonlinear stability of incoherence and collective synchronization in a population of coupled oscillators
• Glassy synchronization in a population of coupled oscillators
• Amplitude expansions for instabilities in populations of globally-coupled oscillators
• Time-periodic phases in populations of nonlinearly coupled oscillators with bimodal frequency distributions
• Dynamics of a globally coupled oscillator array
• Synchronization of Pulse-Coupled Biological Oscillators
• A space-time functional formalism for turbulence
• On the short-time dynamics of networks of Hebbian coupled oscillators

This page was built for publication: Asymptotic description of transients and synchronized states of globally coupled oscillators