Average Conditions for the Permanence of a Bounded Discrete Predator-Prey System. (6th August 2013)

• Record Type: Journal Article
• Authors: Fan, Yong-Hong; Wang, Lin-Lin
• Other Names: Vecchio Antonia Academic Editor.
• Is Part Of: Discrete dynamics in nature and society. Volume 2013(2013)
• Publication Date: 2013-08-06
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/2013/508686
• Languages: English
• ISSNs: 1026-0226

Abstract

Abstract : Average conditions are obtained for the permanence of a discrete bounded system with Holling type II functional response u ( n + 1 ) = u ( n ) e x p { a ( n ) - b ( n ) u ( n ) - c ( n ) v ( n ) / ( u ( n ) + m ( n ) v ( n ) ) }, v ( n + 1 ) = v ( n ) e x p { - d ( n ) + e ( n ) u ( n ) / ( u ( n ) + m ( n ) v ( n ) ) } . The method involves the application of estimates of uniform upper and lower bounds of solutions. When these results are applied to some special delay population models with multiple delays, some new results are obtained and some known results are generalized.