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

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.

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Published: 2019-01-25

How to Cite this Article:

Liu Yu, Xinyu Guan, Xiangdong Xie, Qifa Lin, On the existence and stability of positive periodic solution of a nonautonomous commensal symbiosis model with Michaelis-Menten type harvesting, Communications in Mathematical Biology and Neuroscience, Vol 2019 (2019), Article ID 2

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.

Commun. Math. Biol. Neurosci.

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