Positive periodic solution of a discrete commensal symbiosis model with Holling II functional response
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).- Published
- 14 December 2016
- Volume
- 2016 (2016)
- License
- CC BY 3.0
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.
Cite this article
T. Li, Q. Lin, J. Chen, Positive periodic solution of a discrete commensal symbiosis model with Holling II functional response, Commun. Math. Biol. Neurosci. 2016 (2016), 22.
BibTeX
@article{Li2016,
author = {Li, Tingting and Lin, Qiaoxia and Chen, Jinhuang},
title = {Positive periodic solution of a discrete commensal symbiosis model with Holling II functional response},
journal = {Commun. Math. Biol. Neurosci.},
volume = {2016},
year = {2016},
pages = {22},
doi = {}
}