Open AccessThe Twisting Bifurcations of Double Homoclinic Loops with Resonant Eigenvalues
Author(s) -
Xiaodong Li,
Weipeng Zhang,
Fengjie Geng,
Jicai Huang
Publication year - 2013
Publication title -
abstract and applied analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.228
H-Index - 56
eISSN - 1687-0409
pISSN - 1085-3375
DOI - 10.1155/2013/152518
Subject(s) - homoclinic orbit , homoclinic bifurcation , mathematics , bifurcation , eigenvalues and eigenvectors , heteroclinic orbit , saddle , saddle node bifurcation , mathematical analysis , orbit (dynamics) , bogdanov–takens bifurcation , bifurcation diagram , physics , quantum mechanics , nonlinear system , mathematical optimization , aerospace engineering , engineering
The twisting bifurcations of double homoclinic loops with resonant eigenvalues are investigated in four-dimensional systems. The coexistence or noncoexistence of large 1-homoclinic orbit and large 1-periodic orbit near double homoclinic loops is given. The existence or nonexistence of saddle-node bifurcation surfaces is obtained. Finally, the complete bifurcation diagrams and bifurcation curves are also given under different cases. Moreover, the methods adopted in this paper can be extended to a higher dimensional system
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