Chaotic Systems
For a dynamical system to be classified as chaotic, it must have the following properties:
- it must be sensitive to initial conditions,
- it must be topologically mixing, and
- its periodic orbits must be dense.
Sensitivity to initial conditions means that each point in such a system is arbitrarily closely approximated by other points with significantly different future trajectories. Thus, an arbitrarily small perturbation of the current trajectory may lead to significantly different future behavior.
Read more about this topic: Complex System, Types of Complex Systems
Famous quotes containing the words chaotic and/or systems:
“The attitude that nature is chaotic and that the artist puts order into it is a very absurd point of view, I think. All that we can hope for is to put some order into ourselves.”
—Willem De Kooning (b. 1904)
“What is most original in a man’s nature is often that which is most desperate. Thus new systems are forced on the world by men who simply cannot bear the pain of living with what is. Creators care nothing for their systems except that they be unique. If Hitler had been born in Nazi Germany he wouldn’t have been content to enjoy the atmosphere.”
—Leonard Cohen (b. 1934)