Global Asymptotic Behavior of a Nonautonomous Competitor-Competitor-Mutualist Model. (1st August 2013)

• Record Type: Journal Article
• Authors: Fu, Shengmao; Qu, Fei
• Other Names: Pouso Rodrigo Lopez Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2013(2013)
• Publication Date: 2013-08-01
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2013/812357
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : The global asymptotic behavior of a nonautonomous competitor-competitor-mutualist model is investigated, where all the coefficients are time-dependent and asymptotically approach periodic functions, respectively. Under certain conditions, it is shown that the limit periodic system of this asymptotically periodic model admits two positive periodic solutions ( u 1 T, u 2 T, u 3 T ), ( u 1 T, u 2 T, u 3 T ) such that u i T ≤ u i T ( i = 1, 2, 3 ), and the sector { ( u 1, u 2, u 3 ) : u i T ≤ u i ≤ u i T, i = 1, 2, 3 } is a global attractor of the asymptotically periodic model. In particular, we derive sufficient conditions that guarantee the existence of a positive periodic solution which is globally asymptotically stable.