A commensal symbiosis model with Holling type functional response

Volume 16, Issue 3, pp 364--371
Publication Date: September 15, 2016 Submission Date: June 13, 2016
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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.

•  34C25
•  92D25
•  34D20
•  34D40

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