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

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


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