Positive periodic solution of a discrete Lotka-Volterra commensal symbiosis model
Abstract
Sufficient conditions are obtained for the existence of positive periodic solution of the following discrete Lotka-Volterra commensal symbiosis model
$$\begin{array}{rcl}
x_1(k+1)&=& x_1(k)\exp\big\{ a_1(k)-b_1(k)x_1(k)+c_1(k)x_2(k)\big\},
x_2(k+1)&=& x_2(k)\exp\big\{ a_2(k)-b_2(k)x_2(k)\big\},
\end{array}
$$
where $ \{b_{i}(k)\}, i=1, 2, \{c_1(k)\} $ are all positive $\omega$-periodic sequences, $\omega $ is a fixed positive integer, $\{a_{i}(k)\}$ are $\omega$-periodic sequences, which satisfies $\overline{a}_i=\frac{1}{\omega}\sum\limits_{k=0}^{\omega-1}a_i(k)>0, i=1,2$.- Published
- 20 March 2015
- Volume
- 2015 (2015)
- License
- CC BY 3.0
Copyright © 2015 Xiangdong Xie, Zhansshuai Miao, Yalong Xue. 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
X. Xie, Z. Miao, Y. Xue, Positive periodic solution of a discrete Lotka-Volterra commensal symbiosis model, Commun. Math. Biol. Neurosci. 2015 (2015), 2.
BibTeX
@article{Xie2015,
author = {Xie, Xiangdong and Miao, Zhansshuai and Xue, Yalong},
title = {Positive periodic solution of a discrete Lotka-Volterra commensal symbiosis model},
journal = {Commun. Math. Biol. Neurosci.},
volume = {2015},
year = {2015},
pages = {2},
doi = {}
}