Periodic orbits of competitive and cooperative systems

Hal Smith

doi:10.1016/0022-0396(86)90024-0

Periodic orbits of competitive and cooperative systems

Hal Smith

Research output: Contribution to journal › Article › peer-review

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Abstract

In this paper we consider the existence, location and stability type of periodic orbits of competitive and cooperative systems of autonomous ordinary differential equations. Particular attention is given to the existence of invariant manifolds related to periodic orbits and these results are used to improve a result of Hirsch for three dimensional irreducible competitive and cooperative systems. In particular, the Poincaré-Bendixson theorem holds for such three dimensional systems.

Original language	English (US)
Pages (from-to)	361-373
Number of pages	13
Journal	Journal of Differential Equations
Volume	65
Issue number	3
DOIs	https://doi.org/10.1016/0022-0396(86)90024-0
State	Published - Dec 1986

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/0022-0396(86)90024-0

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title = "Periodic orbits of competitive and cooperative systems",

abstract = "In this paper we consider the existence, location and stability type of periodic orbits of competitive and cooperative systems of autonomous ordinary differential equations. Particular attention is given to the existence of invariant manifolds related to periodic orbits and these results are used to improve a result of Hirsch for three dimensional irreducible competitive and cooperative systems. In particular, the Poincar{\'e}-Bendixson theorem holds for such three dimensional systems.",

author = "Hal Smith",

year = "1986",

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doi = "10.1016/0022-0396(86)90024-0",

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journal = "Journal of Differential Equations",

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PY - 1986/12

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N2 - In this paper we consider the existence, location and stability type of periodic orbits of competitive and cooperative systems of autonomous ordinary differential equations. Particular attention is given to the existence of invariant manifolds related to periodic orbits and these results are used to improve a result of Hirsch for three dimensional irreducible competitive and cooperative systems. In particular, the Poincaré-Bendixson theorem holds for such three dimensional systems.

AB - In this paper we consider the existence, location and stability type of periodic orbits of competitive and cooperative systems of autonomous ordinary differential equations. Particular attention is given to the existence of invariant manifolds related to periodic orbits and these results are used to improve a result of Hirsch for three dimensional irreducible competitive and cooperative systems. In particular, the Poincaré-Bendixson theorem holds for such three dimensional systems.

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U2 - 10.1016/0022-0396(86)90024-0

DO - 10.1016/0022-0396(86)90024-0

M3 - Article

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VL - 65

SP - 361

EP - 373

JO - Journal of Differential Equations

JF - Journal of Differential Equations

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ER -

Periodic orbits of competitive and cooperative systems

Abstract

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