Deterministic Chaos

6.B. Introduction to Chaos

Sensitivity to initial conditions is the bad news of chaos.

Any measurement of the current conditions of a system must have some uncertainty.

Because we cannot specify whether the system is in state S₁ or in some nearby state S₂, we cannot predict behavior very far into the future.

Note this is NOT RANDOM behavior.

In random behavior, knowing the current state, even exactly, we cannot predict the future with certainty.

In deterministic chaos, if we could know the current state exactly, then we could predict the future exactly. (This is the determinisitc part.)

Moreover, approximate knowledge of the present of a random system excludes few, if any, states in the immediate future, while the uncertainties of a chaotic system do not grow large immediately.

We shall see that chaos also contains some good news.

Return to Introduction to Chaos.