%0 Journal Article
%T A commensal symbiosis model with Holling type functional response
%A Wu, Runxin
%A Li, Lin
%A Zhou, Xiaoyan
%J Journal of Mathematics and Computer Science
%D 2016
%V 16
%N 3
%@ ISSN 2008-949X
%F Wu2016
%X A two species commensal symbiosis model with Holling type functional response takes the form
\[\frac{dx}{dt}=x\left(a_1-b_1x+\frac{c_1y^p}{1+y^p}\right),\]
\[\frac{dy}{dt}=y\left(a_2-b_2y\right)\]
is investigated, where \(a_i, b_i, i = 1, 2, p\) and \(c_1\) are all positive constants, \(p \geq 1\). Local and global
stability property of the equilibria is investigated. We also show that depending on the ratio of \(\frac{a_2}{b_2}\),
the first component of the positive equilibrium \(x^*(p)\) may be the increasing or decreasing function
of \(p\) or independent of \(p\). Our study indicates that the unique positive equilibrium is globally stable
and the system always permanent.
%9 journal article
%R 10.22436/jmcs.016.03.06
%U http://dx.doi.org/10.22436/jmcs.016.03.06
%P 364--371