Dynamic behaviors of a periodic Lotka-Volterra commensal symbiosis model with impulsive

Zhanshuai Miao, Xiangdong Xie, Liqiong Pu

Abstract


In this paper, the dynamic behaviors of an impulsive periodic Lotka-Volterra commensal symbiosis model is studied in this paper. Firstly, by constructing a suitable Lyapunov function and using the comparison theorem of impulsive differential equation, some sufficient conditions which ensure the permanence and global attractivity of the system are obtained; Secondly, conditions which guarantee that one species in the system are permanent while the remaining species is driven to extinction is obtained. Thirdly, conditions which ensure the extinction of the system are also obtained. Our results show that, for Lotka-Volterra commensal symbiosis model, impulsive is one of the important reasons that can change the long time behaviors of species.

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Published: 2015-03-20

How to Cite this Article:

Zhanshuai Miao, Xiangdong Xie, Liqiong Pu, Dynamic behaviors of a periodic Lotka-Volterra commensal symbiosis model with impulsive, Communications in Mathematical Biology and Neuroscience, Vol 2015 (2015), Article ID 3

Copyright © 2015 Zhanshuai Miao, Xiangdong Xie, Liqiong Pu. 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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