6.C. Test Functions
|To learn tests of chaos in experimental data, we first analyze
the dynamics of iterates of some simple functions. In general, given a function f(x),
we are interested in predicting the long-term behavior of the orbit|
|x0, x1 = f(x0), x2 = f(x1) =
f2(x0), x3 = f(x2) = f3(x0), ... |
|of the point x0.|
|Can we predict any features of this orbit without
computing the xi?|
|How does the long-term behavior of the orbit depend on the choice
of initial value x0?|
|We shall study these and related questions for these test functions|
|The Tent Map is one of the
simplest of nonlinear maps, its graph is just two straight lines.
|The Logistic Map is a model for a
population growing in an environment with limited resources. Amazingly, there are
questions about these parabolas that cannot be answered.
Return to Deterministic Chaos.