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Homework Help: Is it possible for a chaotic system to have non-chaotic trajectories?

  1. Apr 11, 2013 #1
    1. The problem statement, all variables and given/known data

    I'm working on an assignment about the chaotic behaviour of the Duffing Oscillator, using Wolfram Mathematica, which has a package that can be used to calculate Lyapunov exponents.

    From looking the oscillator up online, I have a set of parameters that result in chaotic behaviour, and for which a Poincare section stabilises after a period of approximately 4 pi.
    I've written a function that calculates the Lyaponuv exponents for the chaotic set of parameters at a variety of initial conditions and then plots the greatest Lyaponuv exponent against the initial conditions.

    The problem is that of my 1024 data points; 10 of them have no positive Lyaponuv exponent, which means that the trajectories aren't chaotic.

    My question is whether this is a computing error, or if it is possible to have non chaotic trajectories in a chaotic system - and because the system is driven; it cant be an equilibrium position causing the anomaly. I haven't

    Any opinions would be much appreciated.

  2. jcsd
  3. Apr 11, 2013 #2


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    Staff: Mentor

    A system can have non-chaotic regions, even if the system is chaotic in most of the parameter space.

    I think the two stable Lagrangian points are a nice example in 3-body orbital mechanics.
  4. Apr 11, 2013 #3
    Thanks - I probably should have known that, I was just put out when my plot of the chaotic-ness of a system turned out to be... chaotic. ;P
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