nullcline
Let
${\dot{x}}_{1}$  $=$  ${f}_{1}({x}_{1},\mathrm{\dots},{x}_{n})$  
$\mathrm{\vdots}$  
${\dot{x}}_{n}$  $=$  ${f}_{n}({x}_{1},\mathrm{\dots},{x}_{n})$ 
be a system of first order ordinary differential equation^{}. The ${x}_{j}$ nullcline is the set of points which satisfy ${f}_{j}({x}_{1},\mathrm{\dots},{x}_{n})=0$. Note that at an intersection point of all the nullclines implies that
$0$  $=$  ${f}_{1}({x}_{1},\mathrm{\dots},{x}_{n})$  
$\mathrm{\vdots}$  
$0$  $=$  ${f}_{n}({x}_{1},\mathrm{\dots},{x}_{n}).$ 
Hence the intersection point of all the nullclines is an equilibrium point of the system.
example:

•
see some qualitative analysis of FitzHughNagumo equation^{} using nullclines
Title  nullcline 

Canonical name  Nullcline 
Date of creation  20130322 14:27:14 
Last modified on  20130322 14:27:14 
Owner  Daume (40) 
Last modified by  Daume (40) 
Numerical id  5 
Author  Daume (40) 
Entry type  Definition 
Classification  msc 34C99 