The Chaos Theory

Question 1

Question 2

Question 3

Purpose

Answer question 1

• To answer that question you could study: Chaos homepage
  In that document we read : Thus, chaos theory lays emphasis not on the disorder of the system--the inherent unpredictability of a system--but on the order inherent in the system--the universal behavior of similar systems. I doubt if that helps.
  
• You could study: The Nature of Deterministic Chaos
  In that document we read:How predictable is a chaotic system? As any deterministic system, it is predictable on a short time scale. But on a long time scale, chaotic systems become unpredictable. Here we read "As any deterministic system". THe question is what do they mean. Are all systems deterministic ? I think that is a very important question.
  May be you find the answer behind the TAB: Non linear dynamics There we read: Nonlinear dynamics became famouse because of the possibility of deterministic chaos, i.e., irregular solutions even though the equation of motion is deterministic.
• To see how difficult it is to define Chaos, please study: Chaos by Wolfram Mathworld
  Here we read: "chaotic systems are distinguished by sensitive dependence on initial conditions and by having evolution through phase space that appears to be quite random."

Answer question 2

• To get an idea please study: Chaos in Dynamical Systems: Second Edition By Edward Ott Here we read at page 2: Under certain conditions the tip of the steel beam was observed to oscillate in a very irregular maner and To show that it is not necessary to invoke such effects, Mon and Holmes considered a simple model for their experiment, namely, the forced Duffing equation in the following form. To read more about this equation please read: Duffing oscillator - Scholarpedia
  

Answer question 3

• First the usage of the word determistic. See also Chaos Theory in Wikepedia

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