Dynamic behaviors of a Holling type commensal symbiosis model with the first species subject to Allee effect
Abstract
A two species commensal symbiosis model with Holling type functional response and the first species subject to Allee effect takes the form
$$
\di\frac{dx}{dt}&=&x\Big(a_1-b_1x\Big)\di\frac{x}{\beta +x}+\di\frac{c_1xy^p}{1+y^p},
\di\frac{dy}{dt}&=&y(a_2-b_2y)
$$
is investigated, where $a_i, b_i, i=1,2$ $p$, $\beta$ and $c_1$ are all positive constants, $p\geq 1$ is a positive integer. Local and global stability property of the equilibria are investigated. Our study indicates that the unique positive equilibrium is globally stable. Also, the final density of the first species is increasing with the Allee effect, this result differs from that obtained for the Holling type commensal symbiosis model with the second species subject to Allee effect.- Published
- 8 February 2019
- Volume
- 2019 (2019)
- License
- CC BY 3.0
Copyright © 2019 Chaoquan Lei. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
C. Lei, Dynamic behaviors of a Holling type commensal symbiosis model with the first species subject to Allee effect, Commun. Math. Biol. Neurosci. 2019 (2019), 3. https://doi.org/10.28919/cmbn/3716
BibTeX
@article{Lei2019,
author = {Lei, Chaoquan},
title = {Dynamic behaviors of a Holling type commensal symbiosis model with the first species subject to Allee effect},
journal = {Commun. Math. Biol. Neurosci.},
volume = {2019},
year = {2019},
pages = {3},
doi = {10.28919/cmbn/3716}
}