Positive periodic solution of a discrete commensal symbiosis model with Holling II functional response

Tingting Li, Qiaoxia Lin, Jinhuang Chen

Abstract


Sufficient conditions are obtained for the existence of positive periodic solution of the following discrete commensal symbiosis 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 $\overline{a}_i=\frac{1}{\omega}\sum\limits_{k=0}^{\omega-1}a_i(k)>0, i=1,2$.The results obtained in this paper generalized the main results of Xiangdong Xie, Zhansshuai Miao, Yalong Xue (Commun. Math. Biol. Neurosci. 2015 (2015), Article ID 2).

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Published: 2016-12-14

How to Cite this Article:

Tingting Li, Qiaoxia Lin, Jinhuang Chen, Positive periodic solution of a discrete commensal symbiosis model with Holling II functional response, Communications in Mathematical Biology and Neuroscience, Vol 2016 (2016), Article ID 22

Copyright © 2016 Tingting Li, Qiaoxia Lin, Jinhuang Chen. 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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