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 , … , x n ) {\displaystyle x_{1}'=f_{1}(x_{1},\ldots ,x_{n})} x 2 ′ = f 2 ( x 1 , … , x n ) {\displaystyle x_{2}'=f_{2}(x_{1},\ldots ,x_{n})} ⋮ {\displaystyle \vdots } x n ′ = f n ( x 1 , … , x n ) {\displaystyle x_{n}'=f_{n}(x_{1},\ldots ,x_{n})} where x ′ {\displaystyle x'} here represents a derivative of x {\displaystyle x} with respect to another parameter, such as time t {\displaystyle t} . The j {\displaystyle j} 'th nullcline is the geometric shape for which x j ′ = 0 {\displaystyle x_{j}'=0} .