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Communications in Mathematical Biology and Neuroscience ISSN 2052-2541

Archives › Volume 2019 (2019)

Commun. Math. Biol. Neurosci. 2019 (2019), Article ID 2

On the existence and stability of positive periodic solution of a nonautonomous commensal symbiosis model with Michaelis-Menten type harvesting

Liu Yu, Xinyu Guan, Xiangdong Xie, Qifa Lin

PDF (205.2 KB) https://doi.org/10.28919/cmbn/3678

Abstract

A non-autonomous commensal symbiosis model of two populations with Michaelis-Menten type harvesting is proposed and studied in this paper. By using a continuation theorem based on Gaines and Mawhin's coincidence degree, we study the global existence of positive periodic solutions of the system. By constructing a suitable Lyapuonov function, sufficient conditions which ensure the global attractivity of the positive periodic solution are obtained. Numeric simulations are carried out to show the feasibility of the main results.

Published
25 January 2019
Volume
2019 (2019)
License
CC BY 3.0

Copyright © 2019 Liu Yu, Xinyu Guan, Xiangdong Xie, 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.

Cite this article

L. Yu, X. Guan, X. Xie, Q. Lin, On the existence and stability of positive periodic solution of a nonautonomous commensal symbiosis model with Michaelis-Menten type harvesting, Commun. Math. Biol. Neurosci. 2019 (2019), 2. https://doi.org/10.28919/cmbn/3678

BibTeX
@article{Yu2019,
  author  = {Yu, Liu and Guan, Xinyu and Xie, Xiangdong and Lin, Qifa},
  title   = {On the existence and stability of positive periodic solution of a nonautonomous commensal symbiosis model with Michaelis-Menten type harvesting},
  journal = {Commun. Math. Biol. Neurosci.},
  volume  = {2019},
  year    = {2019},
  pages   = {2},
  doi     = {10.28919/cmbn/3678}
}