Mathematical models are commonly broken down into numerical or analytical models. Numerical models are those that use some type of numerical timing procedures to figure out a model’s behavior over time. The solution is usually represented by a table or graph. An analytical model usually has a closed solution. In other words, the solution to the equations used to describe changes in the system can be expressed as a mathematical analytic function. Mathematical models can also be divided in other ways. For example, some models are considered deterministic (or a model that always performs the same way for a given set of initial conditions) or stochastic (or a model in which randomness is present).