Global Asymptotic Behavior of a Nonautonomous Competitor-Competitor-Mutualist Model

摘要

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(u1T,u2T,u3T),  (u1T,u2T,u3T)such thatuiT≤uiT  (i=1,2,3), and the sector{(u1,u2,u3):uiT≤ui≤uiT,  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.