### On the existence of positive periodic solution of a amensalism model with Holling II functional response

#### Abstract

Sufficient conditions are obtained for the existence of positive periodic solution of the following discrete amensalism model with Holling II functional response

$$x_1(k+1)= x_1(k)\exp\Big\{ a_1(k)-b_1(k)x_1(k)-\di\frac{c_1(k)x_2(k)}{e_1(k)+f_1(k)x_2(k)}\Big\},$$

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

where $\{b_{i}(k)\}, i=1, 2, \{c_1(k)\}\{e_1(k)\}, \{f_1(k)\}$ 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:**2017-01-17

**How to Cite this Article:**Qiaoxia Lin, Xiaoyan Zhou, On the existence of positive periodic solution of a amensalism model with Holling II functional response, Commun. Math. Biol. Neurosci., 2017 (2017), Article ID 3 Copyright © 2017 Qiaoxia Lin, Xiaoyan Zhou. 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.

Commun. Math. Biol. Neurosci.

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