Global Asymptotic Behavior of a Nonautonomous Competitor-Competitor-Mutualist Model. (1st August 2013) - Fu, Shengmao; Qu, Fei
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.