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ScientificWorldJournal. 2014;2014:716082. doi: 10.1155/2014/716082. Epub 2014 Apr 16.

Bifurcations of nontwisted heteroclinic loop with resonant eigenvalues.

Author information

  • 1School of Science, Linyi University, Linyi, Shandong 276005, China.
  • 2School of Science, Linyi University, Linyi, Shandong 276005, China ; School of Mathematics Science, Shandong Normal University, Jinan 250014, China.

Abstract

By using the foundational solutions of the linear variational equation of the unperturbed system along the heteroclinic orbits to establish the local coordinate systems in the small tubular neighborhoods of the heteroclinic orbits, we study the bifurcation problems of nontwisted heteroclinic loop with resonant eigenvalues. The existence, numbers, and existence regions of 1-heteroclinic loop, 1-homoclinic loop, 1-periodic orbit, 2-fold 1-periodic orbit, and two 1-periodic orbits are obtained. Meanwhile, we give the corresponding bifurcation surfaces.

PMID:
24892076
[PubMed - indexed for MEDLINE]
PMCID:
PMC4032746
Free PMC Article
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