Regular and chaotic transport of discrete solitons in asymmetric potentials

TL;DR

This paper investigates the dynamics of discrete solitons in asymmetric potentials, focusing on how regular and chaotic ratchet transport occurs and can be controlled through various parameters and signals.

Contribution

It provides a detailed analysis of the transition from phase-locked to chaotic transport in discrete solitons, including control methods for chaotic ratchets.

Findings

Transition to chaos occurs via period doubling.

Pinned states can exist within transport regions.

Chaotic ratchets can be controlled with subharmonic signals.

Abstract

Ratchet dynamics of topological solitons of the forced and damped discrete double sine-Gordon system are studied. Directed transport occurring both in regular and in chaotic regions of the phase space and its dependence on damping, amplitude and frequency of the driving, asymmetry parameter, coupling constant, has been extensively investigated. We show that the passage from ratchet phase-locked regime to chaotic ratchets occurs via a period doubling route to chaos and that, quite surprisingly, pinned states can exist inside phase-locking and chaotic transport regions for intermediate values of the coupling constant. The possibility to control chaotic discrete soliton ratchets by means of both small subharmonic signals and more general periodic drivings, has also been investigated.