Saddle-Node Bifurcation

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A saddle-node bifurcation occurs when, by increasing , the graph of the function intersects the line . This is discussed in Example 2.29 in [1] and depicted in the graphic. Intersections with the line correspond to fixed points for the map, which are plotted in the figure at the top right, with solid lines representing stable fixed points and dashed lines representing 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.

Contributed by: Edmon Perkins (March 2011)
After work by: Ali Nayfeh and Balakumar Balachandran
Open content licensed under CC BY-NC-SA



[1] A. H. Nayfeh and B. Balachandran, Applied Nonlinear Dynamics: Analytical, Computational, and Experimental Methods, New York: Wiley, 1995.


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