Discrete vs Continuous Models
Overview
When modeling a system, one of the choices that needs to be made is whether the inputs to the system are modeled as discrete variables or
continuous. A common example is the modeling of
time. A system that takes time to be an integer, i.e., {% \{1,2,3,4 ...\} %} is a discrete model, whereas
time can also be viewed as a contiuous variable taken from the set of
real numbers.
Discrete
A discrete model is a model that takes values on a discrete set (typically time).
That is, the model is a function from a discrete
(countable)
domain to the set of model states.
The evolution of the model is typically governed by an equation that can stated in the following form.
{% X_{t+1} = f(X_t) %}
Continuous
A continuous is a model that takes values on a continuum. That is, the model is a function over
a coninuous
(uncountable)
domain to the set of model states.
Continuous models are often stated in terms of a differential equation. As an example:
{% \frac{d^2f(x)}{dx} + m \frac{df(x)}{dx} = 0 %}
