[sdiy] slightly ot: Chua circuit and chaos

[ASSI]

On Wednesday 12 February 2003 18:15, Grant Richter wrote:
> It's interesting to consider where analogue computation may be
> inherently superior to digital methods.

No, just different. Since there's no way to weed out the noise, no way 
to produce infinite energy or power and it's equally impossible to 
create lossless systems you always end up with limits on precision and 
accuracy. These barriers are much easier to extend with a digital 
system (especially on the part of modeling a lossless system).

> So analogue computation has a much larger set of available solutions
> than digital methods.

Not really and it is also not relevant - you can't read nor implement 
an infinitely precise solution anyway. I may also remind you that 
there's a large set of problems that are supposed to have only integer 
solutions - not surprisingly you're much better off to devise an 
algorithm that directly works in integer (or equivalently, in fixed 
point arithmetic).

> This is very handy for recursive chaotic
> systems where digital methods tend to saturate.

Careless application of certain op-amps yields latching and 
phase-reversal, as does careless application of half-baked numerical 
algorithms. In both worlds it time, experience, insight and skill are 
needed to come up with stable solutions.

> From a mathematical perspective, the soft saturation of an op-amp at
> the rails still contains a larger set of solutions than all the IEEE
> Floating Point numbers. In this case, soft saturation and thermal
> noise is what allows the systems behavior to still be described at
> relative "infinity" (the supply rails) whereas a digital system can
> return only a single solution (largest number).

IEEE floating point has +-infinity, +-0 and a whole bunch of NaN (not a 
number) to signal these conditions where you lose precision and or 
accuracy, but it's up to you to use them wisely. Just as it is up to 
you whether to use (soft) clipping in an amplifier as a feature or try 
hard to avoid it. Somewhere on docs.sun.com you should find a paper 
"What every Scientist should know about floating point" (or google for 
it) - the title says it all. If that's still not enough, you could 
always switch to interval arithmetic.


Achim.
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