Nullcline


In mathematical analysis, nullclines, sometimes called zero-growth isoclines, are encountered in a system of ordinary differential equations
where here represents a derivative of with respect to another parameter, such as time. The 'th nullcline is the geometric shape for which. 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.

History

The definition, though with the name ’directivity curve’, was used in a 1967 article by Endre Simonyi. This article also defined 'directivity vector' as
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.