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Bifurcations of heterodimensional cycles with two saddle points

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  • Geng, Fengjie
  • Zhu, Deming
  • Xu, Yancong

Abstract

The bifurcations of 2-point heterodimensional cycles are investigated in this paper. Under some generic conditions, we establish the existence of one homoclinic loop, one periodic orbit, two periodic orbits, one 2-fold periodic orbit, and the coexistence of one periodic orbit and heteroclinic loop. Some bifurcation patterns different to the case of non-heterodimensional heteroclinic cycles are revealed.

Suggested Citation

  • Geng, Fengjie & Zhu, Deming & Xu, Yancong, 2009. "Bifurcations of heterodimensional cycles with two saddle points," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2063-2075.
    • Handle: RePEc:eee:chsofr:v:39:y:2009:i:5:p:2063-2075
    DOI: 10.1016/j.chaos.2007.06.077
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    References listed on IDEAS

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    1. He, Ji-Huan, 2005. "Limit cycle and bifurcation of nonlinear problems," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 827-833.
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    Cited by:

    1. Lu, Qiuying, 2009. "Non-resonance 3D homoclinic bifurcation with an inclination flip," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2597-2605.

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