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

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

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

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$.

https://doi.org/10.28919/cmbn/2809