  We study the entanglement dynamics of discrete time quantum walks acting on
bounded finite sized graphs. We demonstrate that, depending on system
parameters, the dynamics may be monotonic, oscillatory but highly regular, or
quasi-periodic. While the dynamics of the system are not chaotic since the
system comprises linear evolution, the dynamics often exhibit some features
similar to chaos such as high sensitivity to the system's parameters,
irregularity and infinite periodicity. Our observations are of interest for
entanglement generation, which is one primary use for the quantum walk
formalism. Furthermore, we show that the systems we model can easily be mapped
to optical beamsplitter networks, rendering experimental observation of
quasi-periodic dynamics within reach.
