Fold Bifurcation
المؤلف:
Guckenheimer, J. and Holmes, P
المصدر:
onlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, 3rd ed. New York: Springer-Verlag
الجزء والصفحة:
...
7-10-2021
1367
Fold Bifurcation
Let 
be a one-parameter family of 
map satisfying
then there exist intervals 
, 
and 
such that
1. If 
, then 
has two fixed points in 
with the positive one being unstable and the negative one stable, and
2. If 
, then 
has no fixed points in 
.
This type of bifurcation is known as a fold bifurcation, sometimes also called a saddle-node bifurcation or tangent bifurcation. An example of an equation displaying a fold bifurcation is
(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. 145-149, 1997.
Rasband, S. N. Chaotic Dynamics of Nonlinear Systems. New York: Wiley, pp. 27-28, 1990.
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