Abstract

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

This work is joint with J. Llibre and J. C. Artés.
[1] J.C. Artés and J. Llibre, Statistical measure of quadratic vector fields,"Resenhas", Vol. 6, 2003, pages 85-97.