Abstract
In this paper, a suitable local coordinate system is constructed by using exponential dichotomies and generalizing the Floquet method from periodic systems to nonperiodic systems. Then the Poincaré map is established to solve various problems in homoclinic bifurcations with codimension one or two. Bifurcation diagrams and bifurcation curves are given.
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Project 19771037, supported by NSFC
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Deming, Z. Problems in homoclinic bifurcation with higher dimensions. Acta Mathematica Sinica 14, 341–352 (1998). https://doi.org/10.1007/BF02580437
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DOI: https://doi.org/10.1007/BF02580437