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

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.