â• Kuramoto 2D Phase Vectors ($\theta_i$)
âš¡ Population Spike Raster Plot & Audio Triggers
Phase-Locking Metrics & Auditory-Motor Entrainment
Phase-Locking Value (PLV $R \in [0, 1]$)
0.88
0.0 (Incoherent / Random)
0.5 (Partial Lock)
1.0 (Full Synchronization)
Motor System Pulses Coupled to Rhythm
Auditory-motor basal ganglia-thalamocortical loop synchronized to stimulus
🧠Mechanics of Neural Entrainment
When repetitive rhythmic sound strikes the ear, auditory brainstem neurons fire locked spikes. Cortical populations adjust their natural intrinsic frequencies ($\omega_i$) through phase resets, aligning local population oscillations with the external beat envelope.
🔬 Kuramoto Synchronization Model
Each neuron is modeled as a phase vector $\dot{\theta}_i = \omega_i + \frac{K}{N}\sum \sin(\theta_j - \theta_i) + S \sin(\theta_{stim} - \theta_i) + \eta_i$. As coupling $K$ or stimulus drive $S$ crosses a critical threshold, the order parameter $R$ (PLV) undergoes a phase transition to macroscopic synchrony.