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Poincaré bifurcation of a three-dimensional system

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  • Liu, Xuanliang
  • Han, Maoan

Abstract

Consider a three-dimensional system having an invariant surface. By using bifurcation techniques and analyzing the solutions of bifurcation equations, we study the spatial bifurcation phenomena near a family of periodic orbits and a center in the invariant surface respectively. New formula of Melnikov function is derived and sufficient conditions for the existence of periodic orbits are obtained. An application of our results to a modified van der Pol–Duffing electronic circuit is given.

Suggested Citation

  • Liu, Xuanliang & Han, Maoan, 2005. "Poincaré bifurcation of a three-dimensional system," Chaos, Solitons & Fractals, Elsevier, vol. 23(4), pages 1385-1398.
    • Handle: RePEc:eee:chsofr:v:23:y:2005:i:4:p:1385-1398
    DOI: 10.1016/j.chaos.2004.06.064
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    Cited by:

    1. He, Yuzhu & Fu, Yuxuan & Qiao, Zijian & Kang, Yanmei, 2021. "Chaotic resonance in a fractional-order oscillator system with application to mechanical fault diagnosis," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    2. Ye, Zhiyong & Han, Maoan, 2006. "Singular limit cycle bifurcations to closed orbits and invariant tori," Chaos, Solitons & Fractals, Elsevier, vol. 27(3), pages 758-767.

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