# Math Insight

### Function iteration form definition

A discrete dynamical system is in function iteration form when it is written so that the new value of the state variable is a function of the previous value of the state variable.

If the state variable is $x_n$, then a dynamical system is in function iteration form when it is of the form $$x_{n+1}=f(x_n).$$ For example, the dynamical system $$x_{n+1} = 3 x_n$$ is written in function iteration form with $f(x)=3x.$

An alternative form is difference form, such as $$x_{n+1}-x_n = 2x_n.$$ This dynamical system is identical to the previous one, as one can see by solving for $x_{n+1}$.