Bifurcation of an Orbit Homoclinic to a Hyperbolic Saddle of a Vector Field in

Tiansi Zhang and Dianli Zhao

Discrete Dynamics in Nature and Society, 2015, vol. 2015, 1-6

Abstract:

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.

Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:571838

DOI: 10.1155/2015/571838

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