Non-Linear Dynamics

The mathematical definition of non-linearity contains two important features:

A) A small change in input may produce an incommensurably large change in response.

B) The superposition principle does not hold.

There are a couple of ways to say what this means. One way is to compare a non-linear system to a linear system like a vibrating violin string. The vibrating string has a motion that is the sum of many simpler contributing motions, i.e. the harmonics of the string.

The motions involved in non-linear systems are not simply combinations of a bunch of simpler motions.

Another way is to look at the response of a non-linear system to some kind of vibrating input. A linear system always responds by vibrating at the same frequency as the input. A non-linear system does not usually or necessarily respond at the same frequency as the input.