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Bifurcations of a Homoclinic Orbit to Saddle-Center in Reversible Systems

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  • Zhiqin Qiao
  • Yancong Xu

Abstract

The bifurcations near a primary homoclinic orbit to a saddle-center are investigated in a 4-dimensional reversible system. By establishing a new kind of local moving frame along the primary homoclinic orbit and using the Melnikov functions, the existence and nonexistence of 1-homoclinic orbit and 1-periodic orbit, including symmetric 1-homoclinic orbit and 1-periodic orbit, and their corresponding codimension 1 or codimension 3 surfaces, are obtained.

Suggested Citation

  • Zhiqin Qiao & Yancong Xu, 2012. "Bifurcations of a Homoclinic Orbit to Saddle-Center in Reversible Systems," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-12, November.
    • Handle: RePEc:hin:jnlaaa:678252
    DOI: 10.1155/2012/678252
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