Equilibrium point

The point <math>\tilde \boldsymbol{x}\in R^n<math> is called an equilibrium point for the differential equation <math>\frac{d\boldsymbol{x}}{dt} = \boldsymbol{f}(t,\boldsymbol{x})<math> if <math>\boldsymbol{f}(t,\tilde\boldsymbol{x})=0<math> for all <math>t<math>.

Similarly, the point <math>\tilde \boldsymbol{x}\in R^n<math> is called an equilibrium point for the difference equation <math>\boldsymbol x_{k+1} = \boldsymbol{f}(k,\boldsymbol{x}_k)<math> if <math>\boldsymbol{f}(k,\tilde\boldsymbol{x})=\tilde\boldsymbol x<math> for <math>k=0,1,\ldots<math>.