one of the classic nonlinear 2nd order ODEs is the Duffing equation, which exhibits a supercritical pitchfork: past a certain parameter value, a spiral sink turns to a saddle and sheds a pair of spiral sinks. what's so nice about that? next comes a novel simulation... 1/3pic.twitter.com/Pdeo8sc1GF
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Replying to @robertghrist @blockspins
is the forced oscillator power spectrum distributed into a harmonic set? i.e. power spread across integer multiples of a single base frequency?
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Replying to @robertghrist @PLT_cheater
From a quick google search, the figures on page 9 of http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.865.8764&rep=rep1&type=pdf … suggest that the answer is no (at least for the particular set of parameters they looked at in the chaotic regime...)
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Replying to @blockspins @robertghrist
Thanks! Am I right to understand that M is the time step (smaller time step meaning roughly finer simulation)?
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Replying to @PLT_cheater @robertghrist
I don't believe it's related to the simulation timestep. Their notation is a bit confusing, but I think the superscript letter "M" is just used to denote the quantity defined in Eq. 4.4. The quantity M inside the limit on the right hand side represents an integer which gives ...
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the number of terms used in the sum. As the quantity M goes to infinity, more terms are included in the sum and it approaches an average over "all time".
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Replying to @blockspins @robertghrist
i wonder what the spectrum looks like to the right of the graph - only three peaks are shown (i count DC, i.e. freq=0, as one)
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