Stable structures in parameter space and optimal ratchet transport

• Parameter spaces for ratchet currents of a discrete-time ratchet model is studied.
• Direct relation between ratchet currents and families of Stable Structures is shown.
• Optimal ratchet transport inside Stable Structures is found in the ratchet model.
• Stable Structures align themselves along specific paths on the parameter spaces.
• These structures follow the generic behavior found in nonlinear systems.

Optimal ratchet currents are shown to be directly connected, for all parameters combinations of the ratchet model, to Isoperiodic Stable Structures (ISSs), which are believed to be generic in the parameter spaces of nonlinear dynamical systems. As the ratchet current is more efficient inside the ISSs, which usually are located in preferred direction in the parameter space, it allows us to make crucial statements about the relevant parameters combination to obtain an optimal transport. This is important from the theoretical point of view and for possible experimental realization of efficient currents. We provide an extensive numerical description of the ratchet current throughout the parameters and indicate a trio of ISSs (cusp, non-cusp and shrimp-like), which exist in all pairwise combinations of ratchet parameters. This suggests the general behavior of the ISSs in the context of ratchet transport.