Critical domain problem for the reaction-telegraph equation model of population dynamics
type: Item
instance of: scholarly article
title: Critical domain problem for the reaction-telegraph equation model of population dynamics
zbMATH Open document ID: 1394.92101
author: Weam Alharbi
author: S. V. Petrovskii
published in: Mathematics
publication date: 2018-07-05T00:00:00Z
review text: Summary: A telegraph equation is believed to be an appropriate model of population dynamics as it accounts for the directional persistence of individual animal movement. Being motivated by the problem of habitat fragmentation, which is known to be a major threat to biodiversity that causes species extinction worldwide, we consider the reaction-telegraph equation (i.e., telegraph equation combined with the population growth) on a bounded domain with the goal to establish the conditions of species survival. We first show analytically that, in the case of linear growth, the expression for the domain's critical size coincides with the critical size of the corresponding reaction-diffusion model. We then consider two biologically relevant cases of nonlinear growth, i.e., the logistic growth and the growth with a strong Allee effect. Using extensive numerical simulations, we show that in both cases the critical domain size of the reaction-telegraph equation is larger than the critical domain size of the reaction-diffusion equation. Finally, we discuss possible modifications of the model in order to enhance the positivity of its solutions.
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 35Q92
zbMATH DE Number: 6898751
zbMATH Keywords: animal movement
zbMATH Keywords: fragmented environment
zbMATH Keywords: critical size
zbMATH Keywords: extinction
MaRDI profile type: Publication
full work available at URL: math6040059
OpenAlex ID: W2801119887
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DOI: 10.3390/MATH6040059
description: scientific article; zbMATH DE number 6898751