Modifying the system...

In the mathematical expression defining a system there are normally variables that are the active ingredients in the expression and parameters, which are other mathematical objects, usually numbers. Some parameters may be combined with the variables through mathematical operations like multiplication, addition and so on to build a specific system defining expression. Once the value of this sort of parameter is set it remains constant. To change it is to change the system.

In some expressions there is another sort of parameter that takes on a stream of values to move the system along, as the time, t, is a parameter in the expression x''=a*cos(t)-x*x*x-μ*x'. This stream of value kind of parameter may also be used to create a related family of systems so the effect of the parameter on the system can be easily seen.