Nonexistence of limit cycles for a class of structurally stable quadratic vector fields

J. C. Artés; Jaume Llibre; J. C. Medrado

doi:10.3934/dcds.2007.17.259

Article Contents

2007, Volume 17, Issue 2: 259-270. Doi: 10.3934/dcds.2007.17.259

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Nonexistence of limit cycles for a class of structurally stable quadratic vector fields

1.
Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona
2.
Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia
3.
Instituto de Matemática e Estatística, Universidade Federal de Goiás, 74001–970 Goiânia, Goiás

Received: November 30, 2005

Revised: August 31, 2006

Published: April 2007

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Abstract

The statistical analysis of the structurally stable quadratic vector fields made in [4] shows that the phase portrait 7.1 (see Figure 1) appears without limit cycles, when the other three phase portraits in the same family with low probability sometimes appear with limit cycles. Here we prove that quadratic vector fields having the phase portrait 7.1 have no limit cycles.

Keywords:

limit cycles,
quadratic vector fields.

Mathematics Subject Classification: 58F14, 58F21, 58F30.

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