mathematics-06-00059.pdf (1.09 MB)
Download file

Critical domain problem for the reaction-telegraph equation model of population dynamics

Download (1.09 MB)
journal contribution
posted on 24.05.2018, 14:23 by Weam Alharbi, Sergei Petrovskii
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.

History

Citation

Mathematics, 2018, 6 (4), 59

Author affiliation

/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of Mathematics

Version

VoR (Version of Record)

Published in

Mathematics

Publisher

MDPI

eissn

2227-7390

Acceptance date

13/04/2018

Copyright date

2018

Available date

24/05/2018

Publisher version

http://www.mdpi.com/2227-7390/6/4/59

Language

en

Usage metrics

Categories

Licence

Exports