Transcritical Bifurcation
Let 
be a one-parameter family of 
maps satisfying
 |  |  | (1) |
 | |  | (2) |
 | |  | (3) |
 |  | | (4) |
 | |  | (5) |
Then there are two branches, one stable and one unstable. This Bifurcation is called a transcritical bifurcation. An example of an equation displaying a transcritical bifurcation is
 | (6) |
References
Guckenheimer, J. and Holmes, P. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, 3rd ed. New York: Springer-Verlag, pp. 145 and 149-150, 1997. Rasband, S. N. Chaotic Dynamics of Nonlinear Systems. New York: Wiley, pp. 27-28, 1990.
- Gilbrat's Distribution
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