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A period doubling, quadrupling, etc., that accompanies the onset of Chaos. It represents the sudden appearance of a qualitatively different solution for a nonlinear system as some parameter is varied. Bifurcations come in four basic varieties: Flip Bifurcation, Fold Bifurcation, Pitchfork Bifurcation, and Transcritical Bifurcation (Rasband 1990).
See also Codimension, Feigenbaum Constant, Feigenbaum Function, Flip Bifurcation, Hopf Bifurcation, Logistic Map, Period Doubling, Pitchfork Bifurcation, Tangent Bifurcation, Transcritical Bifurcation
References
Guckenheimer, J. and Holmes, P. ``Local Bifurcations.'' Ch. 3 in
Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, 2nd pr., rev. corr.
New York: Springer-Verlag, pp. 117-165, 1983.
Lichtenberg, A. J. and Lieberman, M. A. ``Bifurcation Phenomena and Transition to Chaos in Dissipative Systems.''
Ch. 7 in Regular and Chaotic Dynamics, 2nd ed. New York: Springer-Verlag, pp. 457-569, 1992.
Rasband, S. N. ``Asymptotic Sets and Bifurcations.'' §2.4 in
Chaotic Dynamics of Nonlinear Systems. New York: Wiley, pp. 25-31, 1990.
Wiggins, S. ``Local Bifurcations.'' Ch. 3 in
Introduction to Applied Nonlinear Dynamical Systems and Chaos.
New York: Springer-Verlag, pp. 253-419, 1990.
Chaos