Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook