Equilibrium point

In mathematics, the point $\tilde \mathbf{x}\in \mathbb{R}^n$ is called an equilibrium point for the differential equation

$\frac{d\mathbf{x}}{dt} = \mathbf{f}(t,\mathbf{x})$

if $\mathbf{f}(t,\tilde\mathbf{x})=0$ for all $t\,\!$ .

Similarly, the point $\tilde \mathbf{x}\in \mathbb{R}^n$ is called an equilibrium point for the difference equation

$\mathbf{x}_{k+1} = \mathbf{f}(k,\mathbf{x}_k)$

if $\mathbf{f}(k,\tilde\mathbf{x})=\tilde\mathbf{x}$ for $k=0,1,\ldots$ .