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 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.