A pitchfork bifurcation occurs when increasing the parameter causes the graph of the function to intersect the line . See Example 2.31 in . Intersections with the line correspond to fixed points for the map, which are plotted in the figure at the top right; solid lines represent stable fixed points and dashed lines represent unstable fixed points. Eigenvalues inside the unit circle correspond to stable fixed points; eigenvalues outside correspond to unstable fixed points. The eigenvalues for the fixed points at particular values of are shown at the bottom.