Quarterly of Applied Mathematics

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

Author(s): Jifa Jiang; Xing Liang
Journal: Quart. Appl. Math. 64 (2006), 483-498.
MSC (2000): Primary 34C12, 37N25; Secondary 92D40
Posted: June 14, 2006
MathSciNet review: 2259050
Retrieve article in: PDF

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Abstract: In this paper, dynamics of the -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 -cells which attract all nonconvergent persistent trajectories. Moreover, it is proved that the Poincaré-Bendixson theorem holds for -species competitive systems with migration.

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