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

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  • Tiansi Zhang
  • Dianli Zhao

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.

Suggested Citation

  • Tiansi Zhang & Dianli Zhao, 2015. "Bifurcation of an Orbit Homoclinic to a Hyperbolic Saddle of a Vector Field in," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-6, February.
    • Handle: RePEc:hin:jnddns:571838
    DOI: 10.1155/2015/571838
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