Nonlinear Dynamics

, Volume 60, Issue 1–2, pp 1–13 | Cite as

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

  • Yancong Xu
  • Deming Zhu
Original Paper


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.


Heterodimensional bifurcation Orbit flip Inclination flip 


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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Department of MathematicsZhejiang UniversityHangzhouChina
  2. 2.Department of MathematicsHangzhou Normal UniversityHangzhouChina
  3. 3.Department of MathematicsEast China Normal UniversityShanghaiChina

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