文章基本信息

标题：Bifurcation of an Orbit Homoclinic to a Hyperbolic Saddle of a Vector Field in
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作者：Tiansi Zhang ; Dianli Zhao
期刊名称：Discrete Dynamics in Nature and Society
印刷版ISSN：1026-0226
电子版ISSN：1607-887X
出版年度：2015
卷号：2015
DOI：10.1155/2015/571838
出版社：Hindawi Publishing Corporation
摘要：We perform a bifurcation analysis of an orbit homoclinic to a hyperbolic saddle of a vector field in . We give an expression of the gap between returning points in a transverse section by renormalizing system, through which we find the existence of homoclinic-doubling bifurcation in the case . Meanwhile, after reparametrizing the parameter, a periodic-doubling bifurcation appears and may be close to a saddle-node bifurcation, if the parameter is varied. These scenarios correspond to the occurrence of chaos. Based on our analysis, bifurcation diagrams of these bifurcations are depicted.