The influence of partial closure for the populations to a harvesting Lotka-Volterra commensalism model

Hang Deng, Xiaoyan Huang

Abstract


The aim of this paper is to investigate the dynamic behaviors of a harvesting Lotka-Volterra commensalism model incorporating partial closure for the populations. By analyzing the characteristic equation of the variational matrix, sufficient conditions which ensure the local stability of the equilibria are obtained; By applying the differential inequality theory and the Dulac criterion, sufficient conditions which ensure the globally asymptotical stability of the equilibria are obtained; Our study shows that depending on the fraction of the stock available for harvesting, the system maybe extinction, partial survival or two species coexist in a stable state. The dynamic behaviors of the system becomes complicated compared with the non-harvesting system. Numeric simulations are carried out to show the feasibility of the main results.

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Published: 2018-05-03

How to Cite this Article:

Hang Deng, Xiaoyan Huang, The influence of partial closure for the populations to a harvesting Lotka-Volterra commensalism model, Communications in Mathematical Biology and Neuroscience, Vol 2018 (2018), Article ID 10

Copyright © 2018 Hang Deng, Xiaoyan Huang. 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.

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