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.
Zhiqin Qiao. Yancong Xu. "Bifurcations of a Homoclinic Orbit to Saddle-Center in Reversible Systems." Abstr. Appl. Anal. 2012 (SI06) 1 - 12, 2012. https://doi.org/10.1155/2012/678252