Let be a one-parameter family of maps satisfying
(1)
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(2)
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(3)
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(4)
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Then there are intervals , , and such that
1. If , then has one unstable fixed point and one stable orbit of period two for , and
2. If , then has a single stable fixed point for .
This type of bifurcation is known as a flip bifurcation. An example of an equation displaying a flip bifurcation is
(5)
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