Hopf bifurcation is a basic tool for finding small amplitude periodic solutions in systems of ordinary differential equations. The kinds of periodic solutions that appear depends on whether the system has symmetry or whether the system is a coupled system associated with a network of ODE. This talks describes some of the types of periodic solutions that can be expected to appear in these contexts and how they can be applied to binocular rivalry. Speaker(s): Marty Golubitsky (Ohio State University)