Pitchfork Bifurcation
Let 
be a one-parameter family of 
map satisfying
 |  |  | (1) |
 | |  | (2) |
 | |  | (3) |
 |  |  | (4) |
 |  |  | (5) |
Then there are intervals having a single stable fixed point and three fixed points (two of which are stable and one ofwhich is unstable). This Bifurcation is called a pitchfork bifurcation. An example of an equation displaying apitchfork 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, p. 31, 1990.
- Disc
- Disconnected Form
- Disconnectivity
- Discontinuity
- Discontinuous
- Discordant Permutation
- Discrepancy Theorem
- Discrete Distribution
- Discrete Fourier Transform
- Discrete Mathematics
- Discrete Set
- Discrete Uniform Distribution
- Discriminant
- Discriminant (Binary Quadratic Form)
- Discriminant (Elliptic Curve)
- Discriminant (Metric)
- Discriminant (Module)
- Discriminant (Polynomial)
- Discriminant (Quadratic Curve)
- Discriminant (Quadratic Form)
- Discriminant (Second Derivative Test)
- Disdyakis Dodecahedron
- Disdyakis Triacontahedron
- Disjoint
- Disjunction