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What is the difference between nonlinearity and chaos, or . . . .

  1. Jan 25, 2007 #1
    What is the difference between nonlinearity and chaos, or is there a difference?
     
  2. jcsd
  3. Feb 7, 2007 #2
    Not all nonlinear systems of eqs are chaotic.
     
  4. Feb 7, 2007 #3
    You're asking the question the wrong way round. A more logical question would be "under what conditions are they the same?"

    As it stands, the shortest answer would be "they're not the same thing". Chaos is a different phenomenon to nonlinearity, but sometimes arises from it.
     
  5. Feb 8, 2007 #4

    vanesch

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    What is sure, is that chaotic systems are non-linear.

    The definition of a chaotic system is:
    - exponential divergence of initially close orbits (Liapunov instability)
    - the state of the system remains in a compact space

    Well, you cannot satisfy both with a linear system: in the case there is exponential divergence, at least one solution will become unbounded.
     
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