Bifurcations of heteroclinic loops

Deming Zhu*, Zhihong Xia

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

60 Scopus citations


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 homo-clinic 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 unproved 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.

Original languageEnglish (US)
Pages (from-to)X6-848
Number of pages12
JournalScience in China, Series A: Mathematics, Physics, Astronomy
Issue number8
StatePublished - Dec 1 1998


  • Heteroclinic orbit
  • Homoclinic bifurcation
  • Periodic orbit bifurcation

ASJC Scopus subject areas

  • Mathematics(all)

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