Simulations of (2) with additional sinusoidal forcing.
<p>In the top panel, snapshots of the probability distribution are taken immediately preceding every third and fourth pulse for the 83 and 94 Hz DBS pulsing, respectively. When there is no DBS pulsing, snapshots are taken at the sinusoidal forcing frequency. As averaging the term associated with the sinusoidal forcing would suggest, we observe desynchronization into three and four clusters for pulsing at 94 and 83 Hz pulsing, respectively. When the DBS pulsing is turned off at <i>t</i> = 8 seconds, the system quickly settles to a synchronized state. The bottom panels show the probability density averaged over multiple snapshots <math><mrow><mi>ρ</mi><mo>¯</mo><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mrow></math> after the initial transient has decayed. Horizontal dashed lines denote troughs of the probability distributions. The probability contained between successive troughs is 0.32, 0.35, and 0.33 in the left panels, and 0.26, 0.26, 0.25, and 0.23 in the right panels.</p