Impact of field heterogeneity on the dynamics of the forced Kuramoto model

Abstract

We studied the impact of field heterogeneity on entrainment in a system of uniformly interacting phase oscillators. Field heterogeneity is shown to induce dynamical heterogeneity in the system. In effect, the heterogeneous field partitions the system into interacting groups of oscillators that feel the same local field strength and phase. Based on numerical and analytical analysis of the explicit dynamical equations derived from the periodically forced Kuramoto model, we found that the heterogeneous field can disrupt entrainment at different field frequencies when compared to the homogeneous field. This transition occurs when the phase- and frequency-locked synchronization between groups of oscillators is broken at a critical field frequency, causing each group to enter a new dynamical state (disrupted state). Strikingly, it is shown that disrupted dynamics can differ between groups.

arXiv comment10 pages, 7 figures

References in corpus (7)

• Synchronization in complex networks
• The Kuramoto model in complex networks
• Low Dimensional Behavior of Large Systems of Globally Coupled Oscillators
• Long Time Evolution of Phase Oscillator Systems
• Stability diagram for the forced Kuramoto model
• Topological phase transition in the periodically forced Kuramoto model
• Competitive Suppression of Synchronization and Non-Monotonic Transitions in Oscillator Communities with Distributed Time Delay