study should also account for the fact that the cat “alpha ”resonance is near 25 Hz ( Nunez, 1995; Rager and Singer, 1998 ). Parameter dependences of features such as entrainment regions, coupled with experiment, potentially enable calibration of parame-ters in the real brain, extending the utility of SSVEPs in probing phys-iology. For example, experiments could map out the phase locking zones as a function of drive frequency and amplitude for direct com-parison with Fig. 3 (e). This would be a particularly sharp test of the theory. Another measure that could be mapped experimentally is LLE; indeed Spiegler et al. (2011) recently performed such an explo-ration in their model. Formal model inversion schemes may also en-able parameter inference by ﬁtting directly to EEG data, particularly when coupled to model selection criteria ( David et al., 2006; Moran et al., 2009; Pinotsis et al., 2012 ), or by using state estimation tech-niques ( Valdes-Sosa et al., 2009 ) for real-time parameter estimation; such methods are highly nontrivial for nonlinear time series and an active area of research. We analyzed the driven dynamics in the vicinity of a stable ﬁxed point, whereas Spiegler et al. (2011) analyzed interactions between an external drive and a pre-existing limit cycle. Recent evidence points toward both types of dynamics occurring in the alpha band with erratic switching between low and high amplitude modes ( Freyer et al., 2009, 2011 ). Thus there is the potential for entrainment properties to ﬂuctu-ate on similar time scales, or perhaps for the mode-switching dynamics to themselves be altered by a periodic drive. Such possibilities could be explored experimentally by measuring the time dependence of entrain-ment and other nonlinear measures. Another important avenue for future theoretical work is to study phase relations between the drive and the ongoing and driven dynam-ics, thus complementing the frequency properties studied here. Phase-resetting of ongoing activity is thought to contribute to some ERP phe-nomena ( Klimesch, 1999 ), and phase coupling in the brain is an area of intense research interest ( Canolty et al., 2006; Varela et al., 2001 ). Retention of spatial variation in activity and intracortical connectiv-ity will enable study of spatiotemporal SSVEP dynamics ( Nunez, 1995; Robinson et al., 2008 ) and gamma activity ( Robinson, 2007 ), which is known to interact with ﬂicker ( Herrmann, 2001 ), although we have shown that neither is necessary to reproduce the entrainment proper-ties discussed here. Spatial variation in both the cortex and the stimuli will also enable exploration of the rich array of patterns associatedwith visual hallucinations ( Bressloff et al., 2002 ). In addition, spatially-varying stimuli such as stationary ( Muthukumaraswamy and Singh, 2008 ) and moving ( Swettenham et al., 2009 ) gratings evoke beta and gamma band ( ≳20 Hz) activity, and visual evoked responses to gratings differ in photosensitive subjects at both alpha and lower frequencies (Porciatti et al., 2000 ). These phenomena could all be explored in the model. Here we focused on visual stimulation, but the same model and analysis should be applicable to other periodic sensory stimuli that pass through the thalamus, with appropriate parameter changes to account for the different thalamic relay nuclei and cortical subnet-works activated. For example, cortical responses to auditory stimula-tion in schizophrenic subjects and healthy controls have been shown to differ in their frequency pro ﬁles ( Vierling-Claassen et al., 2008 ), and such differences could be explored and interpreted with the same techniques as used here. Another potential avenue lies in driv-ing cortical populations directly. This would enable modeling of non-sensory stimulation methods such as transcranial alternating current stimulation (t ACS), which has been shown to interact with ongoing cortical activity in a frequency-dependent manner ( Kanai et al., 2008 ). In summary, the model applied here exhibits the main features of observed EEG responses to periodic visual stimuli, reproducing key nonlinear features of entrainment and harmonic generation, and en-abling quantitative analysis in terms of underlying physiology. 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