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A new proof to Bautin’s theorem

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  • Han, Maoan
  • Zang, Hong
  • Zhang, Tonghua

Abstract

As we know, Bautin proved that a focus of a quadratic system has order at most 3. We give a new and simple proof to this well-known result by using an elementary method. We also use the elementary method to give a necessary and sufficient condition for a quadratic system to have a center.

Suggested Citation

  • Han, Maoan & Zang, Hong & Zhang, Tonghua, 2007. "A new proof to Bautin’s theorem," Chaos, Solitons & Fractals, Elsevier, vol. 31(1), pages 218-223.
    • Handle: RePEc:eee:chsofr:v:31:y:2007:i:1:p:218-223
    DOI: 10.1016/j.chaos.2005.09.051
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    References listed on IDEAS

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    1. Wu, Yuhai & Han, Maoan & Liu, Xuanliang, 2005. "On the study of limit cycles of a cubic polynomials system under Z4-equivariant quintic perturbation," Chaos, Solitons & Fractals, Elsevier, vol. 24(4), pages 999-1012.
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