A dynamical mechanism rooted in the Lorenz system for giant negative and positive mobility of a memory-driven active particle

On applying a small bias force, non-equilibrium systems may respond in paradoxical ways such as with giant negative mobility (GNM) -- a large net drift opposite to the applied bias, or giant positive mobility (GPM) -- an anomalously large drift in the same direction as the applied bias. We consider an idealized model of a memory-driven active particle inspired from experiments with walking/superwalking droplets that takes the form of the celebrated Lorenz system. By adding a small bias force to this Lorenz model, we uncover a mechanism for simultaneous emergence of GNM and GPM in the parameter space. 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 particle's memory. This provides a general dynamical mechanism for the emergence of anomalous transport behaviors for self-driven particles described by low-dimensional autonomous chaotic systems.