In mathematical analysis, nullclines, sometimes called zero-growth isoclines, are encountered in a system of ordinary differential equations where
The equilibrium points of the system are located where all of the nullclines intersect.
In a two-dimensional linear system, the nullclines can be represented by two lines on a two-dimensional plot; in a general two-dimensional system they are arbitrary curves.
The definition, though with the name ’directivity curve’, was used in a 1967 article by Endre Simonyi.
, where P and Q are the dx/dt and dy/dt differential equations, and i and j are the x and y direction unit vectors.
Simonyi developed a new stability test method from these new definitions, and with it he studied differential equations.
This method, beyond the usual stability examinations, provided semi-quantitative results.