This article describes modifications to the psychophysical method of limits that eliminate artifacts associated with the classical method, and thereby indicate whether or not there is perceptual hysteresis. Such hysteresis effects, which are characteristic of dynamical systems, would provide evidence that the near-threshold perception of an attribute is affected by stabilization mechanisms intrinsic to individual neural detectors, and by nonlinear interactions that functionally integrate the detectors when there is sufficient stimulus-initiated activation, thereby stabilizing activation at suprathreshold levels. The article begins with a review of research employing the modified method of limits. It concludes with a model and computational simulations showing how detection instabilities inherent in neural dynamics can create 'activational gaps' between the functionally-integrated and functionally-independent states of neural ensembles, resulting in clear and distinct discrimination between the perception and non-perception of an attribute. The 'self-excitation' threshold for engaging such functionally-integrating detector interactions is differentiated from the traditional 'read-out' threshold (criterion) that determines whether or not the attribute in question can be perceived.