Chaotic Dynamical Systems
- 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)
- 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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