Global asymptotic behavior of a nonautonomous competitor-competitor-mutualist model. (English) Zbl 1470.35360

Fu, Shengmao; Qu, Fei

Abstr. Appl. Anal. 2013, Article ID 812357, 8 p. (2013).

Summary: 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 \(u_{i T} \leq u_i^T\) (\(i = 1,2,3\)), and the sector \(\{(u_1, u_2, u_3) : u_{i T} \leq u_i \leq u_i^T,\, i = 1,2,3 \}\) 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.

MSC:

35Q92	PDEs in connection with biology, chemistry and other natural sciences
92D25	Population dynamics (general)
35K51	Initial-boundary value problems for second-order parabolic systems

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