Subdiffusion, superdiffusion and chemotaxis

TL;DR

This paper introduces nonlinear random walk models for chemotaxis and anomalous transport, deriving population density equations, explaining chemotactic collapse, and demonstrating superdiffusive bacterial behavior with power-law run times.

Contribution

It presents new nonlinear models incorporating residence time and population effects, offering a novel explanation for chemotactic collapse and superdiffusive dynamics.

Findings

Derivation of population density balance equations with residence time dependence

Introduction of anomalous chemotactic sensitivity and aggregation phenomena

Development of a non-Markovian velocity-jump model showing superdiffusive bacterial motion

Abstract

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.