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nullcline : ウィキペディア英語版
nullcline
In mathematical analysis, nullclines, sometimes called zero-growth isoclines, are encountered in a system of ordinary differential equations
:x_1'=f_1(x_1, \ldots, x_n)
:x_2'=f_2(x_1, \ldots, x_n)
::\vdots
:x_n'=f_n(x_1, \ldots, x_n)
where x' here represents a derivative of x with respect to another parameter, such as time t. The j'th nullcline is the geometric shape for which x_j'=0. The fixed 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 Simonyi1. This article also defined 'directivity vector' as
\mathbf = \mathrm(P)\mathbf + \mathrm(Q)\mathbf,
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 semiquantative results.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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