The coupled dynamics of two particles with different limit sets

TL;DR

This paper investigates how coupling two particles with different dynamical behaviors affects directed transport and current suppression, revealing a transition from chaos to hyperchaos linked to current disappearance.

Contribution

It introduces a detailed analysis of how weak coupling influences transport and chaos transitions in a two-particle driven system with distinct attractors.

Findings

Weak coupling reduces current via attractor merging crisis

Complete current suppression coincides with chaos-hyperchaos transition

Coupling influences the emergence of large chaotic attractors

Abstract

We consider a system of two coupled particles evolving in a periodic and spatially symmetric potential under the influence of external driving and damping. The particles are driven individually in such a way that in the uncoupled regime, one particle evolves on a chaotic attractor, while the other evolves on regular periodic attractors. Notably only the latter supports coherent particle transport. The influence of the coupling between the particles is explored, and in particular how it relates to the emergence of a directed current. We show that increasing the (weak) coupling strength subdues the current in a process, which in phase-space, is related to a merging crisis of attractors forming one large chaotic attractor in phase-space. Further, we demonstrate that complete current suppression coincides with a chaos-hyperchaos transition.