It can be very difficult to simulate long-term values accurately (setting smaller tolerances, usually RELTOL first, will cause it to make finer timesteps -- note the simulation will slow down proportionally).
I once tried simulating a theremin (on the transistor level); it works, but the lowest reasonable beat frequency I can seem to simulate is on the order of 2kHz (out of ~1MHz); less and the phase shift slowly rolls around without a well defined waveform (if it were phase locking due to injection, the waveform would be humpy).
Some circuits are, by nature, chaotic. You can, of course, implement the logistic function with samplers and multipliers; anything from the van der Pol oscillator to Lorentz attractors and beyond can be built from analog and calculus function blocks.
People don't always appreciate that peak-current-mode SMPS controllers are inherently chaotic: the graph of duty cycle(s) vs. setpoint has precisely the same form as varying the "r" parameter in the logistic equation. That is, it exhibits a logistic map behavior, and limit cycles. This can be improved, but cannot be eliminated, with slope compensation and feedback. Such circuits whine and hiss when driven into overload.
Tim
--
Deep Friar: a very philosophical monk.
Website: http://seventransistorlabs.com
"rickman" wrote in message
news:keebfh$fii$3@dont-email.me...
>I was simulating a control loop and noticed that it was very regular in
>the small perturbations that occur. I zoomed the scale out and the
>pattern shrunk a bit but as it was zoomed out more another pattern
>started to emerge, similar to the initial, but at a slower rate.
>Continuing to zoom out to wider ranges of time more and more patterns
>showed up, all somewhat familiar, but none quite the same.
>
> I believe that is the sort of thing that is predicted by Chaos Theory. I
> wonder what the fractal number of this data set is?