Dynamic behaviors of a commensal symbiosis model with non-monotonic functional response and non-selective harvesting in a partial closure

Qifa Lin

Abstract


A two species commensal symbiosis model with non-monotonic functional response and non-selective harvesting in a partial closure takes the form

$$

\di\frac{dx}{dt}&=&x\Big(a_1-b_1x+\di\frac{c_1y }{d_1+y^2}\Big)-q_1Emx,

\di\frac{dy}{dt}&=&y(a_2-b_2y)-q_2Emy

$$

is proposed and studied, where $a_i, b_i, q_i, i=1,2$ $c_1$, $E$, $m(0<m<1)$ and $d_1$ are all positive constants. Depending on the range of the parameter $m$, the system may be collapse, or partial survival, or the two species could be coexist in a stable state. We also show that if the system admits a unique positive equilibrium, then it is globally asymptotically stable. By introducing the harvesting term and the reserve area, the system exhibit rich dynamic behaviors. Our results generalize the main results of Chen and Wu (A commensal symbiosis model with non-monotonic functional response, Commun. Math. Biol. Neurosci. 2017 (2017), Article ID 5).

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Published: 2018-02-26

How to Cite this Article:

Qifa Lin, Dynamic behaviors of a commensal symbiosis model with non-monotonic functional response and non-selective harvesting in a partial closure, Communications in Mathematical Biology and Neuroscience, Vol 2018 (2018), Article ID 4

Copyright © 2018 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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