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

Shengmao Fu, Fei Qu
2013 Abstract and Applied Analysis  
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
more » ... r 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.
doi:10.1155/2013/812357 fatcat:zqzbblf4pjetxhgx53aqbgponu