  We present a minimal one-dimensional deterministic continuous dynamical
system that exhibits chaotic behavior and complex transport properties. Our
model is an overdamped rocking ratchet that is periodically kicked with a delta
function potential. We develop an analytical approach that predicts many key
features of the system, such as current reversals, as well as the presence of
chaotic behavior and bifurcation. We show that our approach can be easily
extended to other types of periodic forces, including the square wave.
