Odors of similar intensity may be perceived or not by human subjects. Perceived odors correlate with brain magnetic fields, delayed some hundreds of milliseconds, that are not present for unperceived ones. How might this occur? The endopiriform nucleus is an excitable structure, considered part of the claustrum, that is interconnected with the primary olfactory (piriform) cortex. A procedure called kindling allows the endopiriform nucleus to generate epileptiform activities in vitro that are delayed ∼100 ms after a stimulus, suggesting a mechanism for delayed activity. Using a detailed computational model of the piriform cortex, consistent with an in vitro experiment, we show that the addition of neurons with endopiriform properties could allow similar stimuli to generate either brief responses or prolonged ones, depending on parameters such as a persistent Na+ conductance. Brief responses putatively correlate with lack of conscious perception, and prolonged responses correlate with the presence thereof.