Current basins of attraction in inertia ratchets

Inertia ratchets are characterized by a complex dynamics with multiple current reversals. We recently studied the problem of control of current on inertia ratchets and demonstrated the feasibility of a control method associated with a process of locking to different mean velocity attractors. Here we present the results of a study of the fractal characteristics of basins of attraction for different mean velocities as well as the influence of quenched disorder on the attractors. We find that our previous conjecture that the domains of attraction of the two velocities are intermixed fractals is verified. We also find that the attractor for the negative velocity dissolves as the strength of disorder is increased. These results have important implications for the design of a reliable technique for controlling the particle mean velocities.