Anticipated synchronization in coupled inertia ratchets with time-delayed feedback: a numerical study

TL;DR

This study explores anticipated synchronization in coupled inertia ratchets with time-delayed feedback, demonstrating that the slave system can predict the master’s future dynamics across various transport regimes.

Contribution

It introduces a numerical analysis of anticipated synchronization in inertia ratchets with delay coupling, revealing predictive behavior in directed transport.

Findings

Slave ratchet can predict master’s future response

Synchronization occurs across different transport regimes

Delay coupling parameters influence synchronization quality

Abstract

We investigate anticipated synchronization between two periodically driven deterministic, dissipative inertia ratchets that are able to exhibit directed transport with a finite velocity. The two ratchets interact through an unidirectional delay coupling: one is acting as a master system while the other one represents the slave system. Each of the two dissipative deterministic ratchets is driven externally by a common periodic force. The delay coupling involves two parameters: the coupling strength and the (positive-valued) delay time. We study the synchronization features for the unbounded, current carrying trajectories of the master and the slave, respectively, for four different strengths of the driving amplitude. These in turn characterize differing phase space dynamics of the transporting ratchet dynamics: regular, intermittent and a chaotic transport regime. We find that the slave ratchet can respond in exactly the same way as the master will respond in the future, thereby anticipating the nonlinear directed transport.