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April  2007, 17(2): 259-270. doi: 10.3934/dcds.2007.17.259

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

J. C. Artés 1, , Jaume Llibre 2, and  J. C. Medrado 3,

1. 

Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain
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, Brazil

Received  December 2005 Revised  September 2006 Published  November 2006

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, 58F3.
Citation: J. C. Artés, Jaume Llibre, J. C. Medrado. Nonexistence of limit cycles for a class of structurally stable quadratic vector fields. Discrete & Continuous Dynamical Systems, 2007, 17 (2) : 259-270. doi: 10.3934/dcds.2007.17.259
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