Kinetic and related macroscopic models for chemotaxis on networks

TL;DR

This paper develops and compares kinetic and macroscopic models for chemotaxis on networks, deriving coupling conditions, analyzing their relations, and implementing numerical schemes for directed graphs.

Contribution

It introduces coupling conditions for kinetic models on networks and derives macroscopic approximations, extending asymptotic preserving schemes to directed graphs.

Findings

Kinetic and macroscopic models produce consistent solutions on networks.

Numerical schemes effectively simulate chemotaxis dynamics on complex graphs.

Relations to Keller-Segel models are established and discussed.

Abstract

In this paper we consider kinetic and associated macroscopic models for chemotaxis on a network. Coupling conditions at the nodes of the network for the kinetic problem are presented and used to derive coupling conditions for the macroscopic approximations. The results of the different models are compared and relations to a Keller-Segel model on networks are discussed. For a numerical approximation of the governing equations asymptotic preserving relaxation schemes are extended to directed graphs. Kinetic and macroscopic equations are investigated numerically and their solutions are compared for tripod and more general networks.