Subdiffusion, superdiffusion and chemotaxis

We propose two nonlinear random walk models which are suitable for the analysis of both chemotaxis and anomalous transport. We derive the balance equations for the population density for the case when the transition rate for a random walk depends on residence time, chemotactic substance and population density. We introduce the anomalous chemotactic sensitivity and find anomalous aggregation phenomenon. So we suggest a new explanation of the well-known effect of chemotactic collapse. We develop a non-Markovian “velocity-jump” model and obtain the superdiffusive behavior of bacteria with power law “run” time.