A nullcline of a system of ordinary differential equations is the locus on which one component of the derivative is zero. For the planar autonomous system
 |  |  |
(1)
|
 |  |
(2)
|
the 
-nullcline is 
and the 
-nullcline is 
. Away from an equilibrium
point, the vector field is vertical on an 
-nullcline and horizontal on a 
-nullcline. Their intersections
are precisely the equilibrium points.
For example, the system 
,
has 
-nullclines 
and 
and 
-nullclines 
and 
. Its equilibrium points
are 
and 
. Nullclines divide the phase
plane into regions in which the signs of the components of the vector
field can be examined without solving the differential
equations.
