Directed transport of fractional‑order asymmetrically coupled particle chains in ratchet potential

This work constructs a fractional-order model to describe the dynamics of particle chains with asymmetric coupling subject to non-uniform viscoelastic media and an asymmetric periodic potential. The effects of multiple control parameters on the collective directed motion are systematically investigated. Numerical results reveal that the fractional-order coupled system can achieve directed transport in the absence of external forces and noise driving. Under suitable coupling strengths, the directed transport velocity of the particle chain generally rises as the fractional order increases. We also find that the average velocity of the particle chain exhibits generalized resonance responses with varying system parameters, featuring single-peak, double-peak and multi-peak resonant behaviors. Such resonant behaviors are sensitive to system parameters and originate from the competition between fractional power-law memory and interparticle coupling. Reverse directed transport can be triggered under appropriate parameter combinations, arising from the interplay of asymmetric coupling, medium memory and ratchet potential. Furthermore, under appropriate system parameters, noise can enhance the directed transport velocity, manifesting stochastic resonance in the system.