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Bifurcation Analysis of Homoclinic Flips at Principal Eigenvalues Resonance
College of Science, University of Shanghai for Science and Technology, Shanghai, China
Department of Mathematics, East China Normal University, Shanghai, China
- 1 College of Science, University of Shanghai for Science and Technology, Shanghai, China
- 2 Department of Mathematics, East China Normal University, Shanghai, China
Applied Mathematics·Volume 04 (2013)·Pages 271–278·Published 22 February 2013·DOI10.4236/am.2013.42041
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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 lo cated.
KeywordsOrbit FlipInclination FlipsHomoclinic OrbitResonance
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