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.