Continuous simulation model system behavior by describing the system as a set of differential equations. The behavior is then revealed by graphically solving the system of equations. For example, the tradional approach to studying population stability in ecosystems was defined by the Lotka-Volterra equation:
To solve this equation for a two species interaction requires a some mathematical background. To solve this equation for ten species requires a computer. An analytical solution is nearly impossible in general to derive, so a graphical solution is the next obvious choice. There are a variety of tools on the market solve this kind of equation, for example the Advanced Continuous Simulation Language, or ACSL, is a continuous simulator useful in solving this kind of problem.
An interesting, and interactive, continuous simulation server, Simulation Server can illustrate these points well.
There are a variety of other interesting web sites that provide insight into the use of continuous simulation: