Predicting perceptual boundaries in auditory streaming using delay differential equations

Auditory streaming enables the brain to organize sequences of sounds into perceptually distinct sources, such as following a conversation in a noisy environment. A typical experiment for investigating perceptual boundaries and bistability is to present a subject with a stream containing two alternating tone stimuli. We investigate a model for the processing of such a stream consisting of two identical neural populations of excitatory and inhibitory neurons. The populations are coupled via delayed cross-inhibition and periodically forced with sharp step-type signals (the two-tone stream). We track how the perception boundary depends on threshold selection and establish how boundaries between three different auditory perceptions (single tone vs two tones vs bistability between both perceptions) relate to bifurcations, such as symmetry breaking. We demonstrate that these transitions are governed by symmetry-breaking bifurcations and that the perceptual classification based on neural thresholds is highly sensitive to threshold choice. Our analysis reveals that a fixed threshold is insufficient to capture the true perceptual boundaries and proposes a variable-threshold criterion, informed by the amplitude dynamics of neural responses. Finally, we illustrate how key stimulus parameters, such as tone duration, delay, and internal time scale, shape the boundaries of auditory perceptual organization in the plane of the two most commonly varied experimental parameters, the representation rate, and the difference in tone frequency. These findings offer mechanistic insight into auditory perception dynamics and provide a refined framework for linking neural activity to perceptual organization.