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

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SUMMARY

The discussion centers on the chaotic behavior of the Duffing Oscillator analyzed using Wolfram Mathematica, specifically focusing on the calculation of Lyapunov exponents. The user identified that out of 1024 data points, 10 exhibited non-chaotic trajectories, raising questions about the nature of chaotic systems. It is established that chaotic systems can indeed have non-chaotic regions, as illustrated by examples such as stable Lagrangian points in three-body orbital mechanics. This indicates that the presence of non-chaotic trajectories does not necessarily imply a computational error.

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Ratpigeon
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Homework Statement



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 can't be an equilibrium position causing the anomaly. I haven't

Any opinions would be much appreciated.

Thanks
Ratpigeon
 
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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.
 
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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