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Bifurcations of heterodimensional cycles with one orbit flip and one inclination flip

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Abstract

In this paper, the bifurcations of heterodimensional cycles are investigated by setting up a suitable local coordinate system in a four-dimensional system. Under some ungeneric conditions—one orbit flip and one inclination flip—the persistence of heterodimensional cycles, the existence of homoclinic orbit and a family of periodic orbits, the coexistence of heterodimensional loop and periodic orbit are obtained. Also, the relevant bifurcation surfaces and their existing regions are given.

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang University, Hangzhou, 310027, China

    Yancong Xu

  2. Department of Mathematics, Hangzhou Normal University, Hangzhou, 310036, China

    Yancong Xu

  3. Department of Mathematics, East China Normal University, Shanghai, 200062, China

    Deming Zhu

Authors
  1. Yancong Xu
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  2. Deming Zhu
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Correspondence to Yancong Xu.

Additional information

Supported by National Natural Science Foundation of China (No. 10671069, 60773179) and Foundation of State Key Basic Research 973 Development Programming Item of China (No. 2004CB318000).

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Xu, Y., Zhu, D. Bifurcations of heterodimensional cycles with one orbit flip and one inclination flip. Nonlinear Dyn 60, 1–13 (2010). https://doi.org/10.1007/s11071-009-9575-z

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  • DOI: https://doi.org/10.1007/s11071-009-9575-z

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