C. Diekman and M. Golubitsky
Network Symmetry and Binocular Rivalry Experiments
submitted.
(2013)
Hugh Wilson has proposed treating higher-level decision making as a competition between patterns, and that patterns are coded in the brain as levels of a set of attributes in an appropriately defined network. In this paper, we propose that symmetry-breaking Hopf bifurcation from fusion states in suitably modified Wilson networks, which we call "rivalry networks", can be used in an algorithmic way to explain the surprising percepts that have been observed in a number of binocular rivalry experiments. These rivalry networks modify and extend our initial discussion in Diekma, Golubitsky, and Wang by permitting different kinds of attributes and different types of coupling. We apply this algorithm to psychophysics experiments discussed by Kovacs~ et al, Shevell and Hong, and Suzuki and Grabowecky. We also analyze an experiment proposed by Tong et al with four colored dots (a simplified version of a 24-dot experiment performed in Kovacs et al, and a three-dot analogue of the four-dot experiment. Our algorithm predicts surprising differences between the three- and four-dot experiments.