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Codimension 3 Nontwisted Double Homoclinic Loops Bifurcations with Resonant Eigenvalues

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Abstract

This paper presents the nontwisted double-homoclinic-loop bifurcations with resonant eigenvalues in four dimensional vector fields. The Poincaré map is established to solve various problems in double-homoclinic-loop bifurcations with codimension 3. Bifurcation diagrams and bifurcation curves are given.

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Authors and Affiliations

  1. Department of Mathematics, East China Normal University, Shanghai, 200062, P.R. China

    Weipeng Zhang, Deming Zhu & Dan Liu

  2. School of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin, 130024, P.R. China

    Weipeng Zhang

Authors
  1. Weipeng Zhang
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  2. Deming Zhu
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  3. Dan Liu
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Corresponding author

Correspondence to Deming Zhu.

Additional information

Dedicated to Professor Zhifen Zhang on the occasion of her 80th birthday

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Zhang, W., Zhu, D. & Liu, D. Codimension 3 Nontwisted Double Homoclinic Loops Bifurcations with Resonant Eigenvalues. J Dyn Diff Equat 20, 893–908 (2008). https://doi.org/10.1007/s10884-008-9105-6

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  • DOI: https://doi.org/10.1007/s10884-008-9105-6

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