Bifurcation

In a dynamical system, a bifurcation is 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. The illustration above shows bifurcations (occurring at the location of the blue lines) of the logistic map as the parameter is varied. Bifurcations come in four basic varieties: flip bifurcation, fold bifurcation, pitchfork bifurcation, and transcritical bifurcation (Rasband 1990).

More generally, a bifurcation is a separation of a structure into two branches or parts. For example, in the plot above, the function , where denotes the real part, exhibits a bifurcation along the negative real axis and .