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Pitchfork bifurcation
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Pitchfork bifurcation : ウィキペディア英語版
Pitchfork bifurcation

In bifurcation theory, a field within mathematics, a pitchfork bifurcation is a particular type of local bifurcation. Pitchfork bifurcations, like Hopf bifurcations have two types - supercritical or subcritical.
In continuous dynamical systems described by ODEs—i.e. flows—pitchfork bifurcations occur generically in systems with symmetry.
==Supercritical case==

The normal form of the supercritical pitchfork bifurcation is
: \frac=rx-x^3.
For negative values of r, there is one stable equilibrium at x = 0. For r>0 there is an unstable equilibrium at x = 0, and two stable equilibria at x = \pm\sqrt.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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