Subdiffusion, chemotaxis, and anomalous aggregation

We propose a nonlinear random walk model which is suitable for the analysis of both chemotaxis and anomalous subdiffusive transport. We derive the master 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 an anomalous aggregation phenomenon. So we suggest a different explanation of the well-known effect of chemotactic collapse.