For instance, there are some constants which cannot be changed: G (the gravitational constant) and c (the speed of light in a vacuum) are two examples. Can you think of some others? These constants really deserve their name as constant, and indeed, they are sometimes called universal constants because of their rigidity (and perhaps because of the fact that they work across the universe).

There are other systems that have constants as you let the system run, but you could change these "constants" by modifying the system. For instance, you may do a chemistry experiment in a room with a certain constant temperature T, but if you had a room with the capability of doing so, you could change T and then run the same experiment.

Another example of a constant that could change depending on conditions would be the constant in the logistic population model P' = KP(C - P). In this model, k is a growth constant and C is the carrying capacity of the environment. Depending on what kind of population you are looking at (like bacterial versus rabbits) and what kind of environment the subjects are in (the one populated with predators versus one that is not), you could have different values for these constants.

1. Think of some other situations as above where you have constants that could change depending on the conditions of the experiement.




As mentioned above, "constants" such as these that can change are often called parameters . That is what we will call them from now on. One principle to understand is the following:

Principle: Within a given system or equation, as a parameter changes, so can what happens in the system or equation, sometimes dramatically. Such a dramatic change is called a bifurcation and the values of the parameter where such changes occur are called bifurcation values .