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Transcritical Bifurcation of a Nonlinear Function

​
μ
1.55
A transcritical bifurcation of the function
f(x)=x+μx-
2
x
occurs when increasing the parameter
μ
causes the graph of
f
to intersect the line
y=x
. See Example 2.30 in[1]. 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
μ
are shown at the bottom of the figure.

References

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

Permanent Citation

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