Symptoms of Chaos

We are beginning to sharpen our definition of a chaotic system. First of all, it is a deterministic system. If we observe behavior that we suspect to be the product of a chaotic system, it will also be

difficult to distinguish from random behavior

sensitive to initial conditions

Note well: Neither of these symptoms, on their own, are sufficient to identify chaos.

Note on technical vs. metaphorical uses of terms:

Students of chaotic systems have begun to use the (originally mathematical) terms in a "metaphorical" way. For example, 'bifurcation', defined here as a period doubling has come to be used to refer to any qualititave change. Even the term 'chaos', has become synomous, for some, with 'overwhelming anxiety'.

Metaphors enrich our understanding, and have helped extend nonlinear thinking into new areas. On the other hand, it is important that we are aware of the technical/metaphorical difference.

Next Section: Two & Three-D Dynamic Systems