A fold bifurcation, also called a saddle-node bifurcation or tangent bifurcation, is the bifurcation exhibited by a one-parameter family
of 
maps 
satisfying
![f(0,0)=0
[(partialf)/(partialx)]_(mu=0,x=0)=0
[(partial^2f)/(partialx^2)]_(mu=0,x=0)>0
[(partialf)/(partialmu)]_(mu=0,x=0)>0,](/images/equations/FoldBifurcation/NumberedEquation1.svg) |
for which there exist intervals 
, 
and 
such that
1. If 
,
then 
has two fixed points in 
with the positive one being unstable and
the negative one stable, and
2. If 
,
then 
has no fixed points in 
.
An example of an equation displaying a fold bifurcation is
 |
(Guckenheimer and Holmes 1997, p. 145).
