### Positive periodic solution of a discrete obligate Lotka-Volterra model

#### Abstract

In this paper, sufficient conditions are obtained for the existence of positive periodic solution of the following discrete obligate Lotka-Volterra 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\},\\[4mm]

x_2(k+1)&=& x_2(k)\exp\big\{ a_2(k)-b_2(k)x_2(k)\big\},

\end{array}

$$

where $ \{a_{i}(k)\}, \{b_{i}(k)\}, i=1, 2$ and $\{c_1(k)\} $ are all positive $\omega$-periodic sequences, $\omega $ is a fixed positive integer.**Published:**2015-05-11

**How to Cite this Article:**Fengde Chen, Liqiong Pu, Liya Yang, Positive periodic solution of a discrete obligate Lotka-Volterra model, Communications in Mathematical Biology and Neuroscience, Vol 2015 (2015), Article ID 14 Copyright © 2015 Fengde Chen, Liqiong Pu, Liya Yang. 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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