General coupled-nonlinear-oscillator model for event-related (de)synchronization

Changes in music tempo entrain movement related brain activity

The neural mechanisms of music listening and appreciation are not yet completely understood. Based on the apparent relationship between the beats per minute (tempo) of music and the desire to move (for example feet tapping) induced while listening to that music it is hypothesised that musical tempo may evoke movement related activity in the brain. Participants are instructed to listen, without moving, to a large range of musical pieces spanning a range of styles and tempos during an electroencephalogram (EEG) experiment. Event-related desynchronisation (ERD) in the EEG is observed to correlate significantly with the variance of the tempo of the musical stimuli. This suggests that the dynamics of the beat of the music may induce movement related brain activity in the motor cortex. Furthermore, significant correlations are observed between EEG activity in the alpha band over the motor cortex and the bandpower of the music in the same frequency band over time. This relationship is observed to correlate with the strength of the ERD, suggesting entrainment of motor cortical activity relates to increased ERD strength.

Kuramoto model with time-varying parameters

We analyze the Kuramoto model generalized by explicit consideration of deterministically time-varying parameters. The oscillators' natural frequencies and/or couplings are influenced by external forces with constant or distributed strengths. A dynamics of the collective rhythms is observed, consisting of the external system superimposed on the autonomous one, a characteristic feature of many thermodynamically open systems. This deterministic, stable, continuously time-dependent, collective behavior is fully described, and the external impact to the original system is defined in both the adiabatic and the nonadiabatic limits.