Acta Mathematica Sinica

, Volume 22, Issue 3, pp 855–864 | Cite as

Homoclinic Bifurcation of Orbit Flip with Resonant Principal Eigenvalues

  • Tian Si Zhang
  • De Ming Zhu


Codimension–3 bifurcations of an orbit–flip homoclinic orbit with resonant principal eigenvalues are studied for a four–dimensional system. The existence, number, co–existence and non–coexistence of 1–homoclinic orbit, 1–periodic orbit, 2n–homoclinic orbit and 2n–periodic orbit are obtained. The bifurcation surfaces and existence regions are also given.


Orbit flip Homoclinic orbit Periodic orbit Resonance Principal eigenvalues 

MR (2000) Subject Classification

37C29 34C23 34C37 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Department of MathematicsEast China Normal UniversityShanghai 200062P. R. China

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