Ratchet transport and periodic structures in parameter space

TL;DR

This paper explores the parameter space of a discrete ratchet model, revealing connections between chaotic regions, stable structures, and ratchet current, with implications for understanding transport phenomena in nonlinear systems.

Contribution

It identifies isoperiodic stable structures in the parameter space and links them to ratchet current, including the universal shrimp-shaped structure, extending understanding of transport in nonlinear systems.

Findings

Isoperiodic structures guide ratchet current behavior.

Chaotic domains are connected to stable structures in parameter space.

Transport structures are also found in Langevin equations with oscillating forces.

Abstract

Ratchet models are prominent candidates to describe the transport phenomenum in nature in the absence of external bias. This work analyzes the parameter space of a discrete ratchet model and gives direct connections between chaotic domains and a family of isoperiodic stable structures with the ratchet current. The isoperiodic structures appear along preferred direction in the parameter space giving a guide to follow the current, which usually increases inside the structures but is independent of the corresponding period. One of such structures has the shrimp-shaped form which is known to be an universal structure in the parameter space of dissipative systems. Currents in parameter space provide a direct measure of the momentum asymmetry of the multistable and chaotic attractors times the size of the corresponding basin of attraction. Transport structures are shown to exist in the parameter space of the Langevin equation with an external oscillating force.