Sufficient and Necessary Conditions for the Permanence of a Discrete Model with Beddington-DeAngelis Functional Response. (24th April 2014)

• Record Type: Journal Article
• Authors: Fan, Yong-Hong; Wang, Lin-Lin
• Other Names: Tang Chun-Lei Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2014(2014)
• Publication Date: 2014-04-24
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2014/740895
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : We give a sufficient and necessary condition for the permanence of a discrete model with Beddington-DeAngelis functional response with the formx ( n + 1 ) =x ( n ) e x p { a ( n ) - b ( n ) x ( n ) - c ( n ) y ( n ) /( α ( n ) + β ( n ) x ( n ) + γ ( n ) y ( n ) ) }, y ( n + 1 ) = y ( n ) e x p { - d ( n ) + f ( n ) x ( n ) / ( α ( n ) + β ( n ) x ( n ) + γ ( n ) y ( n ) ) }, wherea ( n ), b ( n ), c ( n ), d ( n ), f ( n ), α ( n ), β ( n ), andγ ( n ) are periodic sequences with the common periodω ; b ( n ) is nonnegative;c ( n ), d ( n ), f ( n ), α ( n ), β ( n ), andγ ( 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 sequenceα ( n ) has great influence on the permanence.