Self-reinforcing directionality generates truncated Lévy walks without the power-law assumption

We introduce a persistent random walk model with finite velocity and self-reinforcing directionality, which explains how exponentially distributed runs self-organize into truncated L\'evy walks observed in active intracellular transport by Chen et al. [Nature Mater., 14, 589 (2015)]. derive the nonhomogeneous space time, hyperbolic partial differential equation for probability density function (PDF) of particle position. This PDF exhibits bimodal (aggregation phenomena) superdiffusive regime, is not classical linear models. find exact solutions first second moments criteria transition to superdiffusion.