A. Homburg and B. Krauskopf, “Resonant Homoclinic Flip Bifurcations,” Journal of Dynamics and Differential Equations, Vol. 12, No. 4, 2000, pp. 807-850. doi:10.1023/A:1009046621861
has been cited by the following article:
TITLE: Bifurcation Analysis of Homoclinic Flips at Principal Eigenvalues Resonance
AUTHORS: Tiansi Zhang, Deming Zhu
KEYWORDS: Orbit Flip; Inclination Flips; Homoclinic Orbit; Resonance
JOURNAL NAME: Applied Mathematics, Vol.4 No.2, February 22, 2013
ABSTRACT: One orbit flip and two inclination flips bifurcation is considered with resonant principal eigenvalues. We introduce a local active coordinate system to establish bifurcation equation and obtain the conditions when the original homoclinic orbit is kept or broken. We also prove the existence and the existence regions of double 1-periodic orbit bifurcation. Moreover, the complicated homoclinic-doubling bifurcations are found and expressed approximately, and are well located.