Math Insight

Difference form definition


A discrete dynamical system is in difference form when it is written so that the left hand side gives the difference in the state variable over one time step.

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

An alternative form is function iteration form, such as $$x_{n+1} = 4x_n.$$ This dynamical system is identical to the previous one, as one can see by subtracting $x_n$ from both sides.