  We undertake a systematic study of the dynamics of Boolean networks to
determine the origin of chaos observed in recent experiments. Networks with
nodes consisting of ideal logic gates are known to display either steady
states, periodic behavior, or an ultraviolet catastrophe where the number of
logic-transition events circulating in the network per unit time grows as a
power-law. In an experiment, non-ideal behavior of the logic gates prevents the
ultraviolet catastrophe and may lead to deterministic chaos. We identify
certain non-ideal features of real logic gates that enable chaos in
experimental networks. We find that short-pulse rejection and the asymmetry
between the logic states tends to engender periodic behavior, at least for the
simplest networks. On the other hand, we find that a memory effect termed
"degradation" can generate chaos. Our results strongly suggest that
deterministic chaos can be expected in a large class of experimental
Boolean-like networks. Such devices may find application in a variety of
technologies requiring fast complex waveforms or flat power spectra, and can be
used as a test-bed for fundamental studies of real-world Boolean-like networks.
