Anomalous transport of a memory-driven active particle

On applying a small bias force, non-equilibrium systems may respond in paradoxical ways such with net motion in the direction opposite to an applied bias force. We consider a minimal model of a memory-driven active particle inspired from experiments with walking and superwalking droplets, whose equation of motion maps to the celebrated Lorenz system. By adding a small bias force to this Lorenz model for the active particle, we uncover a dynamical mechanism for anomalous transport. Within the chaotic sea of the parameter space, a symmetric pair of coexisting asymmetric limit cycles separate and migrate under applied bias force, resulting in anomalous transport behaviors that are sensitive to the active particle's memory. Our work highlights a general dynamical mechanism for the emergence of anomalous transport behaviors for active particles described by low-dimensional nonlinear models.