Neato chaotic equations for analog computers to display?

"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!

ROTFL! At least many of the URL's are. Your browser actually added the ellipses.

In the interest of brevity, I have put a redirection script at:

John Bailey

"James Meyer" wrote

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

Is there a test for chaotically?

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

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.

You tell me.

I'm lost here. I think we are talking about two different things. Best drop it.

Chaos is bounded. Order isn't. "Muddle on Through" Vs "Alles in Ordnung".

"Lou Pecora" wrote

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.

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

I read in sci.electronics.design that Nicholas O. Lindan wrote (in ) about 'Neato chaotic equations for analog computers to display?', on Wed, 22 Dec 2004:

Three gonads? (;-)

Nice one!.

"john jardine" wrote

_Very_ chaotic. Has its attractions, though.

All three are nice.

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

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

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

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

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

Would that be the sign outside a p*rn shop? ;-)

Regards Ian

You have a funny accent. :-)

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Do they repeat themselves?

/BAH

Subtract a hundred and four for e-mail.

That's because time isn't reversible. You just hope and pray that the damned thing is reproducible without a date-time dependency.

One of my thinking games is to "watch" bit flows. The precise circumstances (date-time stamps, physical bit locations, etc.) can never, ever be done exactly the same way twice. Extrapolate this to tech enhancements, societies, and [pssstttt'ing emoticon touches hot button] politics.

/BAH

Subtract a hundred and four for e-mail.

The universe certainly will never contain two identical computer systems. Even the burn-in can't be identical.

You mean one _bottom_ of a barrel. My locals are saying amazing things these days; so much so, I'm struck speechless.

/BAH

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Try tinyurl.com

itself.

had

and

circuit

simulated and

Yo can get a copy of same (which includes SPICE model also) at following link

My query is -->

simulated and

why should we not trust on SPICE results (after all complete analog industry and now SoC design is based on SPICE simulations to a larger extent) ? I know there will be some precision issue and real chaotic trajectory will not be observed but at least it will give a crude idea about the behaviour of the system. I have observed several mathematical equations' set exhibiting chaotic behaviour when modeled using electronic components in SPICE. In fact several electronic designer are working as follows a) Derive / Observe a set of equation which claim to exhibit chaos / hyperchaos.

b) Perform a mathematical analysis which mainly includes deriving Lyapunov for the system and observing if that comes out to be positive.

c) Design an electronic model for the same and proving the trajectory (scrolls etc) using SPICE. They don't design silicon or bread board the system and completely base system on their trust on SPICE. Is the approach wrong ?

When was the double scroll first observed ?

How is Chua's double scroll different from Lorentz or any other scroll ?

Does number of scrolls also specifies the order of randomness ? (whats if one system is having 10 scrolls and other only 1 and they have same Lyapunov Exponent. Does this mean that both have same order of predictability / unpredictability ? Which one is better in terms of applications say to cryptography etc)