Chaotic Dynamics in Kicked Ratchets

A one-dimensional deterministic continuous dynamical system is studied and shown to exhibit chaotic behavior and complex trans- port properties. Our model is an overdamped rocking ratchet with finite dissipation that is periodically kicked with a delta function driving force, without finite inertia terms or temporal or spatial stochastic forces. This is perhaps the simplest model reported in the literature for a ratchet that exhibits a complex chaotic behavior. We present both numerical and analytical results that predict many key features of the system, such as current reversals, as well as the presence of chaotic behavior and bifurcation. In particular, we show that alternate positive and negative delta functions as the unbiased driving force on a ratchet potential produces both synchronized and chaotic regions.