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

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 that uiT≤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.