Advection-diffusion equations for generalized tactic searching behaviors
type: Item
instance of: scholarly article
title: Advection-diffusion equations for generalized tactic searching behaviors
zbMATH Open document ID: 0953.92031
author: Daniel Grünbaum
published in: Journal of Mathematical Biology
publication date: 1999-05-31T00:00:00Z
review text: The paper describes some aspects and consequences of subject movements in population dynamics, especially tactic gradient climbing strategies in terms of partial differential equations for fluxes of populations. The equations analyzed describe the probability density flux for individuals performing a biased random walk with non-random taxis. The objective is to determine the expected or population level effectiveness of various individual-level behavioural responses to environmental heterogeneity. This leads to a Patlack-Keller-Segel-type advection-diffusion equation. The analysis uses methods described by \textit{W. Alt} [J. Math. Biol. 9, 147-177 (1980; Zbl 0434.92001)] by a biased random walk. The derivation generalizes the turning behaviour specified either in terms of the turning time distribution or of turning rates. An example shows how to examine the effectiveness of two classes of stochastic responses of searching animals to randomly distributed discrete resource patches.
Mathematics Subject Classification ID: 92D50
Mathematics Subject Classification ID: 92D40
Mathematics Subject Classification ID: 35B05
Mathematics Subject Classification ID: 60G50
zbMATH DE Number: 1271807
zbMATH Keywords: diffusion
zbMATH Keywords: taxis
zbMATH Keywords: kinesis
zbMATH Keywords: random walks
zbMATH Keywords: turning time distribution
zbMATH Keywords: advection-diffusion equation
reviewed by: Hans-Peter Altenburg
MaRDI profile type: Publication
full work available at URL: s002850050145
OpenAlex ID: W2023667918
DOI: 10.1007/S002850050145
description: scientific article; zbMATH DE number 1271807