Convergence results and a Poincaré-Bendixson trichotomy for asymptotically autonomous differential equations

Horst Thieme

doi:10.1007/BF00173267

Convergence results and a Poincaré-Bendixson trichotomy for asymptotically autonomous differential equations

Horst Thieme

Mathematical and Statistical Sciences, School of (SoMSS)

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

568 Scopus citations

Abstract

Conditions are presented under which the solutions of asymptotically autonomous differential equations have the same asymptotic behavior as the solutions of the associated limit equations. An example displays that this does not hold in general.

Original language	English (US)
Pages (from-to)	755-763
Number of pages	9
Journal	Journal Of Mathematical Biology
Volume	30
Issue number	7
DOIs	https://doi.org/10.1007/BF00173267
State	Published - Aug 1992

Keywords

Asymptotic behavior
Butler-McGehee lemma
Chemostat
Dynamical systems
Epidemics

ASJC Scopus subject areas

Modeling and Simulation
Agricultural and Biological Sciences (miscellaneous)
Applied Mathematics

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10.1007/BF00173267

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title = "Convergence results and a Poincar{\'e}-Bendixson trichotomy for asymptotically autonomous differential equations",

abstract = "Conditions are presented under which the solutions of asymptotically autonomous differential equations have the same asymptotic behavior as the solutions of the associated limit equations. An example displays that this does not hold in general.",

keywords = "Asymptotic behavior, Butler-McGehee lemma, Chemostat, Dynamical systems, Epidemics",

author = "Horst Thieme",

year = "1992",

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AB - Conditions are presented under which the solutions of asymptotically autonomous differential equations have the same asymptotic behavior as the solutions of the associated limit equations. An example displays that this does not hold in general.

KW - Asymptotic behavior

KW - Butler-McGehee lemma

KW - Chemostat

KW - Dynamical systems

KW - Epidemics

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Convergence results and a Poincaré-Bendixson trichotomy for asymptotically autonomous differential equations

Abstract

Keywords

ASJC Scopus subject areas

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