A summary of the dynamic behavior of the proton bunches in the Brookhaven Alternating Gradient Synchrotron (AGS) has been given previously. In these reports, the usual linearization of the differential equations involved has been made and the theory was restricted to well bunched beams. The linearized approach is no longer valid at transition where the actual phase angle of the bunch can differ appreciably for a short time from the stable phase angle Φ₀. In this report the non-linearity of the differential equations for phase oscillations will no longer be neglected. At transition the beam is slow enough so that the electronics of the bootstrap system can be considered as being ideal and the radius servo loop can be characterized by one time constant. Under these assumptions the analysis can be carried out in a two-dimensional phase plane. The essential new result will be the short existence of a stable equilibrium point for the bunch motion not coinciding with Φ₀. The results here derived have been tested experimentally and at least a qualitative agreement was found. However, the conclusions are no more valid if debunching takes place since we have still neglected the finite bunch width.