## Abstract and Applied Analysis

### Sufficient and Necessary Conditions for the Permanence of a Discrete Model with Beddington-DeAngelis Functional Response

#### Abstract

We give a sufficient and necessary condition for the permanence of a discrete model with Beddington-DeAngelis functional response with the form $x(n+\mathrm{1})$ = $x(n)\mathrm{\text{e}}\mathrm{\text{x}}\mathrm{\text{p}}\{a(n)-b(n)x(n)-c(n)y(n)$/$(\alpha (n)+\beta (n)x(n)+\gamma (n)y(n))\},\mathrm{}y(n+\mathrm{1})=y(n)\mathrm{\text{e}}\mathrm{\text{x}}\mathrm{\text{p}}\{-d(n)+f(n)x(n)/(\alpha (n)+\beta (n)x(n)+\gamma (n)y(n))\},$ where $a(n),$ $b(n),$ $c(n),$ $d(n),$ $f(n),$ $\alpha (n),$ $\beta (n)$, and $\gamma (n)$ are periodic sequences with the common period $\omega ;$ $b(n)$ is nonnegative; $c(n),$ $d(n),$ $f(n),$ $\alpha (n),$ $\beta (n)$, and $\gamma (n)$ are positive. It is because of the difference between the comparison theorem for discrete system and its corresponding continuous system that an additional condition should be considered. In addition, through some analysis on the limit case of this system, we find that the sequence $\alpha (n)$ has great influence on the permanence.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 740895, 9 pages.

Dates
First available in Project Euclid: 2 October 2014

https://projecteuclid.org/euclid.aaa/1412276935

Digital Object Identifier
doi:10.1155/2014/740895

Mathematical Reviews number (MathSciNet)
MR3200803

Zentralblatt MATH identifier
07022991

#### Citation

Fan, Yong-Hong; Wang, Lin-Lin. Sufficient and Necessary Conditions for the Permanence of a Discrete Model with Beddington-DeAngelis Functional Response. Abstr. Appl. Anal. 2014 (2014), Article ID 740895, 9 pages. doi:10.1155/2014/740895. https://projecteuclid.org/euclid.aaa/1412276935