Competitive systems with migration and the Poincaré-Bendixson theorem for a 4-dimensional case

Jiang, Jifa; Liang, Xing

doi:10.1090/S0033-569X-06-01016-0

Authors: Jifa Jiang and Xing Liang
Journal: Quart. Appl. Math. 64 (2006), 483-498
MSC (2000): Primary 34C12, 37N25; Secondary 92D40
DOI: https://doi.org/10.1090/S0033-569X-06-01016-0
Published electronically: June 14, 2006
MathSciNet review: 2259050
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Abstract: In this paper, dynamics of the $n$-species competitive system with migration is studied. It is proved that if the Jacobian matrix of the system is irreducible at every point in Int $\mathbb {R}^{2n}_+$, then there is a defined countable family of invariant $(2n-1)$-cells which attract all nonconvergent persistent trajectories. Moreover, it is proved that the Poincaré-Bendixson theorem holds for $2$-species competitive systems with migration.

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