Nullcline

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

${\displaystyle x_{1}'=f_{1}(x_{1},\ldots ,x_{n})}$

${\displaystyle x_{2}'=f_{2}(x_{1},\ldots ,x_{n})}$

${\displaystyle \vdots }$

${\displaystyle x_{n}'=f_{n}(x_{1},\ldots ,x_{n})}$

where ${\displaystyle x'}$ here represents a derivative of ${\displaystyle x}$ with respect to another parameter, such as time ${\displaystyle t}$. The ${\displaystyle j}$'th nullcline is the geometric shape for which ${\displaystyle x_{j}'=0}$. 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.