Methods to assess binocular rivalry with periodic stimuli

Binocular rivalry occurs when the two eyes are presented with incompatible stimuli and perception alternates between these two stimuli. This phenomenon has been investigated in two types of experiments: (1) Traditional experiments where the stimulus is fixed, (2) eye-swap experiments in which the stimulus periodically swaps between eyes many times per second (Logothetis et al. in Nature 380(6575):621-624, 1996). In spite of the rapid swapping between eyes, perception can be stable for many seconds with specific stimulus parameter configurations. Wilson introduced a two-stage, hierarchical model to explain both types of experiments (Wilson in Proc. Natl. Acad. Sci. 100(24):14499-14503, 2003). Wilson's model and other rivalry models have been only studied with bifurcation analysis for fixed inputs and different types of dynamical behavior that can occur with periodically forcing inputs have not been investigated. Here we report (1) a more complete description of the complex dynamics in the unforced Wilson model, (2) a bifurcation analysis with periodic forcing. Previously, bifurcation analysis of the Wilson model with fixed inputs has revealed three main types of dynamical behaviors: Winner-takes-all (WTA), Rivalry oscillations (RIV), Simultaneous activity (SIM). Our results have revealed richer dynamics including mixed-mode oscillations (MMOs) and a period-doubling cascade, which corresponds to low-amplitude WTA (LAWTA) oscillations. On the other hand, studying rivalry models with numerical continuation shows that periodic forcing with high frequency (e.g. 18 Hz, known as flicker) modulates the three main types of behaviors that occur with fixed inputs with forcing frequency (WTA-Mod, RIV-Mod, SIM-Mod). However, dynamical behavior will be different with low frequency periodic forcing (around 1.5 Hz, so-called swap). In addition to WTA-Mod and SIM-Mod, cycle skipping, multi-cycle skipping and chaotic dynamics are found. This research provides a framework for either assessing binocular rivalry models to check consistency with empirical results, or for better understanding neural dynamics and mechanisms necessary to implement a minimal binocular rivalry model.