Abstract competitive systems and orbital stability in

Authors:
Rafael Ortega and Luis Ángel Sánchez

Journal:
Proc. Amer. Math. Soc. **128** (2000), 2911-2919

MSC (2000):
Primary 34C25, 34C12, 34D20

DOI:
https://doi.org/10.1090/S0002-9939-00-05610-0

Published electronically:
April 7, 2000

MathSciNet review:
1701688

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Competitive autonomous systems in have the remarkable property of verifying an analogue of the Poincaré-Bendixon theorem for planar equations. This fact allows us to prove the existence of orbitally stable closed orbits for those systems under easily checkable hypothesis. Our aim is to introduce, by changing the ordering in , a new class of autonomous systems for which the preceding results directly extend. As a consequence we shall reinterpret some of the results of R. A. Smith in terms of the theory of monotone systems.

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Additional Information

**Rafael Ortega**

Affiliation:
Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain

Email:
rortega@goliat.ugr.es

**Luis Ángel Sánchez**

Affiliation:
Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain

Email:
lasperez@goliat.ugr.es

DOI:
https://doi.org/10.1090/S0002-9939-00-05610-0

Keywords:
Orbital stability,
competitive systems,
monotone systems

Received by editor(s):
November 3, 1998

Published electronically:
April 7, 2000

Additional Notes:
This research was supported by DGES PB95-1203 (Spain)

Communicated by:
Hal L. Smith

Article copyright:
© Copyright 2000
American Mathematical Society