Bifurcations of heteroclinic loops

  • Deming Zhu
  • Zhihong Xia


By generalizing the Floquet method from periodic systems to systems with exponential dichotomy, a local coordinate system is established in a neighborhood of the heteroclinic loop Γ to study the bifurcation problems of homoclinic and periodic orbits. Asymptotic expressions of the bifurcation surfaces and their relative positions are given. The results obtained in literature concerned with the 1-hom bifurcation surfaces are improved and extended to the nontransversal case. Existence regions of the 1-per orbits bifurcated from Γ are described, and the uniqueness and incoexistence of the 1-hom and 1-per orbit and the inexistence of the 2-hom and 2-per orbit are also obtained.


heteroclinic orbit homoclinlc bifurcation periodic orbit bifurcation 


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Copyright information

© Science in China Press 1998

Authors and Affiliations

  • Deming Zhu
    • 1
  • Zhihong Xia
    • 2
  1. 1.Department of MathematicsEast China Normal UniversityShanghaiChina
  2. 2.Department of MathematicsNorthwestern UniversityEvanstonUSA

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