Transcritical Bifurcation of a Nonlinear Function
A transcritical bifurcation of the function occurs when increasing the parameter causes the graph of to intersect the line . See Example 2.30 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 to unstable fixed points. The eigenvalues for the fixed points at particular values of are shown at the bottom of the figure.
 A. H. Nayfeh and B. Balachandran, Applied Nonlinear Dynamics: Analytical, Computational, and Experimental Methods, New York: Wiley, 1995.