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Abstract and Applied Analysis
Volume 2014, Article ID 740895, 9 pages
Research Article

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

School of Mathematics and Statistics Science, Ludong University, Yantai, Shandong 264025, China

Received 18 December 2013; Revised 20 March 2014; Accepted 24 March 2014; Published 24 April 2014

Academic Editor: Chun-Lei Tang

Copyright © 2014 Yong-Hong Fan and Lin-Lin Wang. 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.


We give a sufficient and necessary condition for the permanence of a discrete model with Beddington-DeAngelis functional response with the form = / where , and are periodic sequences with the common period is nonnegative; , and 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 has great influence on the permanence.