Classic oscillator simulations.

Abstract

A. Set up of a Wilson-Cowan oscillator model (see Methods) with parameters set at: a = b = c = 10, d = -2 and (E,I) = (1.6, -2.9). The acoustic envelope of a stimulus trial drives the excitatory population with coupling determined by parameter k. The phase of the oscillator at the expected time of the last tone according to absolute timing (ABS) or the relative timing algorithm (REL) is computed on each trial. B. Phase concentration of predicted phases, ABS in purple and REL in blue across trials at a restricted range of stimulus rates (240 to 260 ms). Better phase concentration would lead to a more accurate prediction of the probe time relative to the corresponding perceptual timing mechanism. Shaded areas mark significant differences using the circular K test to test for significant differences in concentration (correcting for multiple comparisons using the false discovery rate Benjamini & Hochberg, 1995). Insets represent example concentrations at = 0.15, left, and = 2.0, right. C. Same as b but with a range of stimulus rates that reflects the statistics of the experiment (210 to 290 ms). D. Model task performance compared between Absolute and Relative algorithms in the restricted range of stimulus rates (240 to 260 ms). The difference in slope parameters fitting a Logistic regression between phase of the oscillator at probe time and the correct response defined either by absolute or relative perceptual timing mechanisms (see Methods). Polynomial fit and confidence shown in black line and gray patch respectively. Second order determined through AIC Model selection. E. Same as D with the broader range of stimulus rates (210 to 290 ms). F. Phase Response Curve of the Wilson-Cowan oscillator in response to a single 100 ms tone at a range of coupling parameters (from 0.02 to 1). Blue lines refer to coupling constants that lead to significantly higher concentration for the relative prediction, Purple to those significantly higher for the absolute one and gray to those with no significant difference between them. Phase response curves consistent with relative timing show a topologically distinct behavior than the other two categories. Data for S2 Fig can be found in S7 Data. (PNG)</p