Deterministic inhomogeneous ratchet in a periodic potential

We numerically investigate the deterministic dynamics of a one-dimensional particle in a symmetric periodic potential under the influence of an external periodic force. Additionally, we introduce asymmetry into the system by applying a space–time dependent frictional force. A simple physical example of the theoretical problem studied might be the propagation of a longitudinal sound wave in a symmetric periodic system. This leads to compression and rarefaction in the medium, resulting in particles being subjected to a damping force that periodically fluctuates in both space and time. Our objective is to investigate whether, during this process, net particle transport can be achieved within the considered inhomogeneous deterministic ratchet system and explore the necessary conditions for this to occur. We identify the various regimes of particle motion as manifested by the particle mean velocity as a function of the driving force amplitude. There are primarily three regimes: periodic intrawell, periodic interwell, and chaotic regimes observed. Ratchet effect is observed in both the periodic interwell and chaotic regimes; however, our focus lies on studying particle dynamics within the periodic interwell regime and exploring any relation between the constant ensemble-averaged current in that regime and the frequencies of the frictional force and applied external force. Furthermore, we demonstrate multiple dynamical attractors present under certain circumstances in the system analysed.