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Bifurcation Analysis of Homoclinic Flips at Principal Eigenvalues Resonance

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DOI: 10.4236/am.2013.42041    3,162 Downloads   5,741 Views   Citations


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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The authors declare no conflicts of interest.

Cite this paper

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.


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