EconPapers    
Economics at your fingertips  
 

Critical Domain Problem for the Reaction–Telegraph Equation Model of Population Dynamics

Weam Alharbi () and Sergei Petrovskii ()
Additional contact information
Weam Alharbi: Department of Mathematics, University of Leicester, University Road, Leicester LE1 7RH, UK
Sergei Petrovskii: Department of Mathematics, University of Leicester, University Road, Leicester LE1 7RH, UK

Mathematics, 2018, vol. 6, issue 4, 1-15

Abstract: 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.

Keywords: animal movement; fragmented environment; critical size; extinction (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1) Track citations by RSS feed

Downloads: (external link)
https://www.mdpi.com/2227-7390/6/4/59/pdf (application/pdf)
https://www.mdpi.com/2227-7390/6/4/59/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:6:y:2018:i:4:p:59-:d:141488

Access Statistics for this article

Mathematics is currently edited by Ms. Patty Hu

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().

 
Page updated 2022-03-26
Handle: RePEc:gam:jmathe:v:6:y:2018:i:4:p:59-:d:141488