Noise-induced walking patterns on ratchets

We propose a model for a walker moving on an asymmetric periodic ratchet potential mediated by noise. The walker has two feet that make steps in patterns. These are represented as two finite size particles coupled through a double-well potential. The system contains three noise sources: two independent white noises, modeling thermal noise, and exponentially correlated common noise. In the case where only white noise is present, we perform a bifurcation analysis which reveals different walking patterns available for various parameter settings. Numerical simulations showed the existence of current reversals and significant changes in the effective diffusion constant and in the synchronization index. We obtained an optimal transport, characterized by a maximum dimensionless ratio of the current and effective diffusion (Peclet number), when the periodicity of the ratchet potential coincides with the equilibrium distance between the two feet.