Pitchfork Bifurcation
المؤلف:
Guckenheimer, J. and Holmes, P.
المصدر:
Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, 3rd ed. New York: Springer-Verlag
الجزء والصفحة:
...
12-10-2021
1703
Pitchfork Bifurcation
Let 
be a one-parameter family of 
maps satisfying
(Rasband 1990, p. 31), although condition (1) can actually be relaxed slightly. Then there are intervals having a single stable fixed point and three fixed points (two of which are stable and one of which is unstable). This type of bifurcation is called a pitchfork bifurcation.
An example of an equation displaying a pitchfork bifurcation is
 |
(5)
|
(Guckenheimer and Holmes 1997, p. 145).
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, p. 31, 1990.
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