### A Holling type commensal symbiosis model involving Allee effect

#### Abstract

A two species commensal symbiosis model with Holling type functional response and Allee effect on the second species takes the form

$$

\di\frac{dx}{dt}&=&x\Big(a_1-b_1x+\di\frac{c_1y^p}{1+y^p}\Big),

\di\frac{dy}{dt}&=&y(a_2-b_2y)\di\frac{y}{u+y}

$$

is investigated, where $a_i, b_i, i=1,2$ $p$, $u$ and $c_1$ are all positive constants, $p\geq 1$. Local and global stability property of the equilibria is investigated.Our study indicates that the unique positive equilibrium is globally stable and the system always permanent, consequently, Allee effect has no influence on the final density of the species. However, numeric simulations show that the stronger the Allee effect, the longer the for the system to reach its stable steady-state solution.

**Published:**2018-03-16

**How to Cite this Article:**Runxin Wu, Lin Li, Qifa Lin, A Holling type commensal symbiosis model involving Allee effect, Communications in Mathematical Biology and Neuroscience, Vol 2018 (2018), Article ID 6 Copyright © 2018 Runxin Wu, Lin Li, Qifa Lin. 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.

Commun. Math. Biol. Neurosci.

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