[sdiy] slightly ot: Chua circuit and chaos

[Czech Martin]

>>We simply use these numbers for every day engineering.
>>Are we allowed to do so?
>>Is the concept of real numbers a good model for what's
>>really going on?

>This will be covered by any decent university comp sci course. It's usually 
>called something like 'computing with approximate numbers.'
>
>You can't learn scientific programming to degree level without being aware 
>of the limitations of only having a certain level of accuracy. That's 
>certainly true for DSP programming as well as other things.

The above statement refers not to limited accuracy in computers.
The question is, if real numbers are used in all their infinity,
are they a good model for certain systems?
Charge is represented by a natural (whole) number of electrons or ions
and so on.

As you say, "chaos" seems to collapse if real numbers are not
used. Insofar it is allowed to ask if chaos really exists
outside mathematical models (where it exists for sure).

The problem of computational error is certainly another important
issue.

So far we have:

systems which behave with natural numbers (e.g. number of electrons),
are translated into D.E. with real numbers,
these are solved using rational numbers as computer approximations
of real numbers and difference equations as approximations
of D.E., and finally this is believed to approximate the
real world problem. So no wonder that this sometimes does not work.

As far as "chaotic" or nonlinear dynamics are involved, I have
never seen a basic course on numeric computation discussing these
issues.

Also basic texts on "chaos" seem to do not even mention these problems.


m.c.