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:
“Our chaotic economic situation has convinced so many of our young people that there is no room for them. They become uncertain and restless and morbid; they grab at false promises, embrace false gods and judge things by treacherous values. Their insecurity makes them believe that tomorrow doesn’t matter and the ineffectualness of their lives makes them deny the ideals which we of an older generation acknowledged.”
—Hortense Odlum (1892–?)
“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)