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

Zhiqin Qiao and Yancong Xu

Abstract and Applied Analysis, 2012, vol. 2012, 1-12

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.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:678252

DOI: 10.1155/2012/678252

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