Pitchfork Bifurcation in Dynamical Systems
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.
 A. H. Nayfeh and B. Balachandran, Applied Nonlinear Dynamics: Analytical, Computational, and Experimental Methods, New York: Wiley, 1995.