A commensal symbiosis model with Holling type functional response
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Authors
Runxin Wu
- College of Mathematics and Physics, Fujian University of Technology, Fuzhou, Fujian, 350014, P. R. China.
Lin Li
- College of Mathematics and Physics, Fujian University of Technology, Fuzhou, Fujian, 350014, P. R. China.
Xiaoyan Zhou
- Public Foundation Department, Fuzhou Polytechnic, Fuzhou, Fujian, 352300, P. R. China.
Abstract
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.
Share and Cite
ISRP Style
Runxin Wu, Lin Li, Xiaoyan Zhou, A commensal symbiosis model with Holling type functional response, Journal of Mathematics and Computer Science, 16 (2016), no. 3, 364--371
AMA Style
Wu Runxin, Li Lin, Zhou Xiaoyan, A commensal symbiosis model with Holling type functional response. J Math Comput SCI-JM. (2016); 16(3):364--371
Chicago/Turabian Style
Wu, Runxin, Li, Lin, Zhou, Xiaoyan. "A commensal symbiosis model with Holling type functional response." Journal of Mathematics and Computer Science, 16, no. 3 (2016): 364--371
Keywords
- Commensal symbiosis model
- stability.
MSC
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