What is "nullcline"

In mathematical analysis, nullclines, sometimes called zero-growth isoclines, are encountered in a system of ordinary differential equations

xʹ = f(x, …, x)

xʹ = f(x, …, x)

where xʹ 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 xʹ = 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.