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Codimension 3 Nontwisted Double Homoclinic Loops Bifurcations with Resonant Eigenvalues |
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| Authors: | Weipeng Zhang Deming Zhu Dan Liu |
| Institution: | (1) Department of Mathematics, East China Normal University, Shanghai, 200062, P.R. China;(2) School of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin, 130024, P.R. China |
| 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. Dedicated to Professor Zhifen Zhang on the occasion of her 80th birthday |
| Keywords: | Double homoclinic loops Resonant eigenvalues Periodic orbit Bifurcation |
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