Generalized Rivalry Networks: Reduction, Dynamics, and Derived Patterns
Casey Diekman (Mathematical Biosciences Institute, The Ohio State University)
(February 28, 2013 10:20 AM - 11:15 AM)
Binocular rivalry is the alternation in visual perception that can occur when the two eyes are presented with different images. Hugh Wilson proposed a class of neuronal network models that generalize rivalry to multiple competing patterns. The networks are assumed to have learned several patterns, and rivalry is identified with time periodic states that have periods of dominance of different patterns. In this talk we will use the theory of coupled cell systems to identify conditions under which networks with two learned patterns reduce to certain recent models of binocular rivalry where much of the dynamics are organized by a Takens-Bogdanov singularity. We also show that Wilson networks support patterns that were not learned, which we call derived. This is important because there is evidence for perception of derived patterns during several binocular rivalry experiments in the literature. We construct Wilson networks for these experiments and use symmetry breaking to make predictions regarding states that a subject might perceive.