### 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:**2015-03-20

**How to Cite this Article:**Xiangdong Xie, Zhansshuai Miao, Yalong Xue, Positive periodic solution of a discrete Lotka-Volterra commensal symbiosis model, Communications in Mathematical Biology and Neuroscience, Vol 2015 (2015), Article ID 2 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.

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