also show the actual spectrum without multiplication by f). The model parameters here are modi ﬁed slightly from those in Fig. 1 (b) to better maintain the resemblance to key features of the data, such as widths of entrainment regimes. This parameter adjustment is needed because removing harmonics from the drive in going from square to sine wave reduces power at higher frequencies. This mod-iﬁes the EEG spectra (such as by changing the mix of subharmonics generated), which can be approximately compensated for by small adjustment of model parameters. We stress that this step is carriedout solely to probe the underlying mechanisms with more clarity and does not affect the level of agreement between the square-wave case and experiment found in the Square wave drive section. Entrainment of the alpha frequency to 2 f Doccurs over a narrow range where 2 f D≈fα; just above this drive frequency there is an en-hancement where the background activity is shifted slightly down-wards. Sum and difference frequencies f±=|f D±fα| are generated by nonlinear interactions (other than entrainment) between the drive and background activity. This phenomenon is well-known as Fig. 3. Model results for ( νee,νei,νes,νse,νsr,νsn,νre,νrs)=(1. 3,-2. 9, 0. 13, 2. 9,-0. 57, 1. 0, 0. 67, 2. 9) m V s, Φn=2. 8s-1, other parameters as in Fig. 1 (b). (a) Spectral response for f D=0-50 Hz, labeled as in Fig. 1 (b) but with grayscale range extended to show lower-level peaks, and without multiplying by f. (b) Detail of (a); Features A-C are discussed in the text. (c) Bicoherence for SSVEP at f D=30 Hz and parameters of (a). (d) Turning points (after transients) of noise-free time series vs. Φnforf D=20 Hz and parameters of (a). Green and red points show bistable solutions obtained by continuation up and down in Φn, respectively; yellow shows where red would otherwise overplot green. (e) Phase-locking zones for noise-free driven system initially at a stable ﬁxed point for parameters of (a). (f) Largest Lyapunov exponent (LLE) vs. Φnfor time series corresponding to the forward continuation in (d). Dark points in (a)-(c) correspond to high values. 1951 J. A. Roberts, P. A. Robinson / Neuro Image 62 (2012) 1947-1955