Flip Bifurcation/Examples/Arbitrary Example 1

Example of Flip Bifurcation

Consider the mapping:

$\forall x \in \R: \map {T_\lambda} x = x^2 - \paren {1 + \lambda}$

$T_\lambda$ has a flip bifurcation at $\lambda = 0$.

Proof

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Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): bifurcation
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): bifurcation