| Projected dynamical system theory represents a bridge between the static worlds of variational inequalities and equilibrium problems, and the dynamical world of ordinary differential equations. A projected dynamical system is given by the flow of a projected differential equation, an ordinary differential equation whose trajectories are restricted to a constraint set K. Projected differential equations are defined by a nonlinear and discontinuous vector field and therefore standard ordinary differential equations theory does not apply. The formal study of projected dynamical systems began in the 1990s and the study of periodic cycles for projected dynamical systems began in 2006. In this thesis, we summarize several known results and present a few new results regarding the existence of periodic cycles for projected dynamical systems. |
