Study of visual stimulus waveforms via forced van der Pol oscillator model for SSVEP-based brain-computer interfaces

Visual stimulus design is a central problem for practical brain-computer interfaces (BCIs) based on steady state visually evoked potentials (SSVEPs). In this study, we compare the performances of three differing stimulus waveforms: sine wave, square wave of 50% duty cycle, and the output of the autonomous van der Pol oscillator. The human brain SSVEP is modeled with a forced van der Pol oscillator in which these three driving waveforms are individually applied. In doing so, we use binary search to yield equation parameters that predictably generates frequency maxima in the desired ratio. We compare the minimum amplitude required for each stimulus to activate a corresponding local maximum within the relevant frequency band. We then compute and graph a suitably defined signal-to-noise ratio (SNR) in relation to stimulus frequency for the three waveforms in order to ascertain their relative rates of synchronization. This theoretical exploration has its aim to provide a guideline to the development of an optimal visual stimulus pattern for use in real life SSVEP-based BCI applications.