Chaos in Kicked Ratchets

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.