Homoclinic bifurcation with nonhyperbolic equilibria |
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Authors: | Xingbo Liu Xianlong FuDeming Zhu |
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Affiliation: | Department of Mathematics, East China Normal University, 200062, Shanghai, China |
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Abstract: | The problem of homoclinic bifurcation is studied for a high dimensional system with nonhyperbolic equilibria. By constructing local coordinate systems near the unperturbed homoclinic orbit, Poincaré maps for the new system are established. Then the persistence of the homoclinic orbit and the bifurcation of the periodic orbit for the system accompanied with pitchfork bifurcation are obtained. Some known results are extended. |
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Keywords: | 34C23 34C37 37C29 |
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