A flip bifurcation is the bifurcation exhibited by a one-parameter family of 
maps 
satisfying
 |  |  |
(1)
|
![[(partialf)/(partialx)]_(mu=0,x=0)](/images/equations/FlipBifurcation/Inline6.svg) |  |  |
(2)
|
![[(partial^2f)/(partialx^2)]_(mu=0,x=0)](/images/equations/FlipBifurcation/Inline9.svg) |  |  |
(3)
|
![[(partial^3f)/(partialx^3)]_(mu=0,x=0)](/images/equations/FlipBifurcation/Inline12.svg) |  |  |
(4)
|
for which 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 
.
An example of an equation displaying a flip bifurcation is
 |
(5)
|
