Bifurcation Analysis of Homoclinic Flips at Principal Eigenvalues Resonance

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.

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T. Zhang and D. Zhu, "Bifurcation Analysis of Homoclinic Flips at Principal Eigenvalues Resonance," Applied Mathematics, Vol. 4 No. 2, 2013, pp. 271-278. doi: 10.4236/am.2013.42041.

Conflicts of Interest

The authors declare no conflicts of interest.

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