A commensal symbiosis model with Holling type functional response


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

  • Share on Facebook
  • Share on Twitter
  • Share on LinkedIn
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


MSC


References