## Chaotic Dynamical Systems

## Central Themes

#### Fall 1999

- Simple, deterministic systems can produce random
behavior. Example: logistic equation.

- Complicated, large systems can have relatively simple dynamics.
Example: Random boolean networks with K=2 have only sqrt(N)
attractors.

- Fractals can be produced by deterministic and stochastic systems.
Examples: making snowflakes via a deterministic rule; flipping
coins to build a Sierpinsky triangle.

- Mathematical models are sometimes not used for prediction, but
instead to gain a qualitative feel for a system.

- Universality. Some features of dynamical systems are universal.
These features as quantitatively the same for lots of different
dynamical systems and can (and have) been measured experimentally.

- The mathematics of dynamical systems comes in many different
forms, flavors, and styles.

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[Dave]
[Chaotic
Dynamics]
[COA]
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Web page maintained by dave@hornacek.coa.edu.