High dimensionality and complexity are the main difficulties of the study over network dynamics. Recently, Wilten Nicola proposed the mean field theory to research the bifurcations that the full networks display. Here, we use his approach on the birdsong neural network. Our previous work has shown that AFP could adjust the synapse conductance of nucleus RA and change RA’s firing patterns, eventually leading to song degradation. To understand the dynamical principle behind this, we use a technique to reduce the RA network to a mean field model, in the form of a system of switching ordinary differential equations. Numerical results have shown that the mean field equations can qualitatively and quantitatively describe the behavior of nucleus RA. Based on the non-smooth bifurcation analysis of the mean field model, we determine that there is a subcritical-Andronov-Hopf bifurcation at a particular stimulation, which can explain the role of AFP during song degradation. The results indicate that we can see AFP’s adjustment in RA synapse conductance as the adjustment of initial value in the bistable system. More precisely, during song degradation, the mean field system would transform to a stable node (corresponding to distorted songs) rather than a stable limit cycle (corresponding to normal songs).