Phase synchronization in tilted deterministic ratchets

TL;DR

This paper investigates phase synchronization in a deterministic tilted ratchet system, demonstrating how an intrinsic oscillator can entrain with external periodic forcing, characterized by Arnold tongues affecting transport.

Contribution

It introduces a linear phase definition for the system and analyzes synchronization regions, providing new insights into ratchet transport mechanisms.

Findings

Intrinsic frequency can be entrained with external forcing.

Synchronization regions form Arnold tongues in parameter space.

Transport properties are influenced by synchronization phenomena.

Abstract

We study phase synchronization for a ratchet system. We consider the deterministic dynamics of a particle in a tilted ratchet potential with an external periodic forcing, in the overdamped case. The ratchet potential has to be tilted in order to obtain a rotator or self-sustained nonlinear oscillator in the absence of external periodic forcing. This oscillator has an intrinsic frequency that can be entrained with the frequency of the external driving. We introduced a linear phase through a set of discrete time events and the associated average frequency, and show that this frequency can be synchronized with the frequency of the external driving. In this way, we can properly characterize the phenomenon of synchronization through Arnold tongues, which represent regions of synchronization in parameter space, and discuss their implications for transport in ratchets.