wrote
> has anyone created a chaotic circuit in
> SPICE?

The model may quickly run into precision limits and
produce false results.

--
Nicholas O. Lindan, Cleveland, Ohio
Consulting Engineer: Electronics; Informatics; Photonics.
Remove spaces etc. to reply: n o lindan at net com dot com
psst.. want to buy an f-stop timer? nolindan.com/da/fstop/

From:	Foobar T. Clown
Subject:	Re: Neato chaotic equations for analog computers to display?
Date:	Wed, 22 Dec 2004 15:14:17 GMT

Nicholas O. Lindan wrote:

> wrote
>
>>has anyone created a chaotic circuit in
>>SPICE?
>
>
> The model may quickly run into precision limits and
> produce false results.

"False results?" What does that mean? Is there a 'true' result? If
you ACTUALLY built a chaotic oscillator out of ACTUAL electronic
components and started it up, would its result be true? How about if
you built two of them, and tried your very hardest to start them both up
under the same identical conditions, would they both continue to produce
the same output forever? If not, which one would be the 'true' one?

-- Foo!

From:	Nicholas O. Lindan
Subject:	Re: Neato chaotic equations for analog computers to display?
Date:	Wed, 22 Dec 2004 16:16:20 GMT

"Foobar T. Clown"
> Nicholas O. Lindan wrote:
> > >has anyone created a chaotic circuit in
> > >SPICE?
> > The model may quickly run into precision limits and
> > produce false results.

> "False results?" What does that mean? Is there a 'true' result?

To a set of differential equations? I always thought so.

> If you ACTUALLY built a chaotic oscillator out of ACTUAL electronic
> components and started it up, would its result be true?

By definition a physical circuit behaves in a true manner for itself.

It may not agree with the Spice model what with rounding
errors in the SPICE and noise in the electronics.

> If not, which one would be the 'true' one?

You tell me.

--
Nicholas O. Lindan, Cleveland, Ohio
Consulting Engineer: Electronics; Informatics; Photonics.
Remove spaces etc. to reply: n o lindan at net com dot com
psst.. want to buy an f-stop timer? nolindan.com/da/fstop/

From:	James Meyer
Subject:	Re: Neato chaotic equations for analog computers to display?
Date:	Thu, 23 Dec 2004 01:54:47 GMT

On Wed, 22 Dec 2004 16:16:20 GMT, "Nicholas O. Lindan" wroth:

>
>By definition a physical circuit behaves in a true manner for itself.
>
>It may not agree with the Spice model what with rounding
>errors in the SPICE and noise in the electronics.
>
>> If not, which one would be the 'true' one?
>
>You tell me.

The circuit model I used with PSpice was the "Chua" circuit. It had
already been constructed with op-amps, resistors, and capacitors and
demonstrated chaotic behavior. I was curious to see if a simulated circuit
would be chaotic as well. I was surprised to find that the simulated and "real"
circuits behaved the same way.

Jim

From:	Nicholas O. Lindan
Subject:	Re: Neato chaotic equations for analog computers to display?
Date:	Thu, 23 Dec 2004 20:10:52 GMT

"James Meyer" wrote
> I wrote:
> >By definition a physical circuit behaves in a true manner for itself.
> >It may not agree with the Spice model what with rounding
> >errors in the SPICE and noise in the electronics.
> The circuit model I used with PSpice was the "Chua" circuit. It had
> already been constructed with op-amps, resistors, and capacitors and
> demonstrated chaotic behavior. I was curious to see if a simulated circuit
> would be chaotic as well. I was surprised to find that the simulated and
"real"
> circuits behaved the same way.

Since that time (ancient history, almost a 1/2 day ago) it has been
discovered by way of Google that there are (seem to be?) 3 forms of
chaotic behavior:

o Can be numerically modeled and the model is always
converging to the equation.

o Can be numerically modeled to any length of time if
given enough precision.

o Can not be modeled.

The act of the model following (or not) the closed form of the
equation is called 'shadowing'.

The name fits, as I am sure 'Only the Shadow Knows'.

Yes, mail me the spice model and I'll get hold of the eval copy
of MicroSim. I would like to see it. The only reason to hang
around on Usenet is to learn something new (AFAICT the usual lesson
is learning you are wrong).

--
Nicholas O. Lindan, Cleveland, Ohio
Consulting Engineer: Electronics; Informatics; Photonics.
Remove spaces etc. to reply: n o lindan at net com dot com
psst.. want to buy an f-stop timer? nolindan.com/da/fstop/

From:	James Meyer
Subject:	Re: Neato chaotic equations for analog computers to display?
Date:	Wed, 22 Dec 2004 12:53:52 GMT

On Wed, 22 Dec 2004 03:02:14 GMT, "Nicholas O. Lindan" wroth:

> wrote
>> has anyone created a chaotic circuit in
>> SPICE?
>
>The model may quickly run into precision limits and
>produce false results.

I have a spice model that demonstrates chaos. The simulation will run
as long as you care to let it run and will produce chaotic results that are
stable.

Jim

From:	Lou Pecora
Subject:	Re: Neato chaotic equations for analog computers to display?
Date:	Wed, 22 Dec 2004 10:55:42 -0500

In article ,
James Meyer wrote:

> [on SPICE:] I have a spice model that demonstrates chaos. The simulation will run
> as long as you care to let it run and will produce chaotic results that are
> stable.
>
> Jim

There are a lot of systems that behavior according to the Shadowing
Theorem (see Yorke, et. al and probably others) wherein, roughly, for
any calculated trajectory there is a real trajectory that follows it
within some epsilon for some specified length of time (arbitrarily
long). So models will not 'run well' for a while and then diverge off
into 'junk.' So, you're right, you can run the model as long as you
like.

-- Lou Pecora (my views are my own)

From:	Nicholas O. Lindan
Subject:	Re: Neato chaotic equations for analog computers to display?
Date:	Wed, 22 Dec 2004 17:27:25 GMT

"Lou Pecora" wrote

> There are a lot of systems that behavior according to the Shadowing
> Theorem (see Yorke, et. al and probably others) wherein, roughly, for
> any calculated trajectory there is a real trajectory that follows it
> within some epsilon for some specified length of time (arbitrarily
> long).

There are three cases: Sometimes you can; Sometimes rounding error
gets in the way; Sometimes you can't no matter what.

Quoting from: Younghae et. al., 2003, "Universal
and nonuniversal features in shadowing dynamics...", Arizona
State University

An understanding of the shadowing dynamics relies on
the mathematical notion of hyperbolicity. Roughly, the dynamics
is hyperbolic on a chaotic set if at each point of the
trajectory, the tangent space can be split into expanding and
contracting subspaces and the angle between them is
bounded away from zero. Furthermore, the expanding subspace
evolves into the expanding one along the trajectory
and the same holds for the contracting subspace. Otherwise,
the set is nonhyperbolic. The following results have been
established.

1 Hyperbolic chaotic systems permit infinite shadowing
of numerical trajectories.

2 For nonhyperbolic chaotic systems with tangencies
(i.e., points at which the expanding and contracting directions
coincide), shadowing can be expected for a finite
amount of time that depends on the computer roundoff error.

3 If the dimensions of the expanding and contracting
subspaces are not constant on different parts of the invariant
set, i.e., if there is unstable dimension variability, then shadowing
of numerical trajectories for relatively long time is
impossible. The severe obstruction to shadowing in the
presence of unstable-dimension variability appears to be
common in high-dimensional chaotic systems, i.e., those
with multiple positive Lyapunov exponents.

What's needed is hyperbolic weather. With the way the snow is
coming down I think I will have to settle for hypobaric.

--
Nicholas O. Lindan, Cleveland, Ohio
Consulting Engineer: Electronics; Informatics; Photonics.
Remove spaces etc. to reply: n o lindan at net com dot com
psst.. want to buy an f-stop timer? nolindan.com/da/fstop/

From:	Nicholas O. Lindan
Subject:	Re: Neato chaotic equations for analog computers to display?
Date:	Wed, 22 Dec 2004 15:27:37 GMT

"James Meyer" wrote

> I have a spice model that demonstrates chaos. The simulation will run
> as long as you care to let it run and will produce chaotic results that are
> stable.

Stable as in they get stuck or as in they don't zoom off into hyperspace.

That the results are chaotic I grant you. But are they are accurate
after a sufficiently large number of iterations?

I found round-off errors propagate like mad and changing from
32 to 64 to 80 bit reals made for very different behavior.

Is there a test for chaotically?

--
Nicholas O. Lindan, Cleveland, Ohio
Consulting Engineer: Electronics; Informatics; Photonics.
Remove spaces etc. to reply: n o lindan at net com dot com
psst.. want to buy an f-stop timer? nolindan.com/da/fstop/

From:	James Meyer
Subject:	Re: Neato chaotic equations for analog computers to display?
Date:	Thu, 23 Dec 2004 01:47:07 GMT

On Wed, 22 Dec 2004 15:27:37 GMT, "Nicholas O. Lindan" wroth:

>"James Meyer" wrote
>
>> I have a spice model that demonstrates chaos. The simulation will run
>> as long as you care to let it run and will produce chaotic results that are
>> stable.
>
>Stable as in they get stuck or as in they don't zoom off into hyperspace.

Stable as in the output remains chaotic regardless of the length of time
that the simulation runs.

>
>That the results are chaotic I grant you. But are they are accurate
>after a sufficiently large number of iterations?

Entirely accurate.

If you have or can get Microsim's PSpice evaluation version 8.0, I can
send you my model and you can judge for yourself.

Jim