title: Synchronization and plateau splitting of coupled oscillators with long-range power-law interactions.
abstract: We investigate synchronization and plateau splitting of coupled oscillators on a one-dimensional lattice with long-range interactions that decay over distance as a power law. We show that in the thermodynamic limit the dynamics of systems of coupled oscillators with power-law exponent α≤1 is identical to that of the all-to-all coupling case. For α>1, oscillatory behavior of the phase coherence appears as a result of single plateau splitting into multiple plateaus. A coarse-graining method is used to investigate the onset of plateau splitting. We analyze a simple oscillatory state formed by two plateaus in detail and propose a systematic approach to predict the onset of plateau splitting. The prediction of breaking points of plateau splitting is in quantitatively good agreement with numerical simulations.
authors.affiliation: Department of Physics, National Tsing-Hua University, 30013 Hsinchu, Taiwan.
authors.forename: Huan-Yu
authors.initials: HY
authors.lastname: Kuo
authors.affiliation: Department of Physics, National Tsing-Hua University, 30013 Hsinchu, Taiwan.
authors.forename: Kuo-An
authors.initials: KA
authors.lastname: Wu