[sdiy] VC Chaos

[ASSI]

On Sonntag, 28. November 2004 21:36, Ian Fritz wrote:
> The circuit I posted is an autonomous system (self-oscillating,
> non-driven), based on another recent paper by Elwakil.  

Based on my limited experience with Chua type circuits from long ago I 
believe that non-autonomous systems may have greater utility for 
musical purposes. After all the chaos occuring naturally in real 
instruments is always (always means I know no counterexample - how's 
that for a proof? ;-) in response to an external force. One of my ideas 
is to keep the oscillator tonal by almost, but not quite injection 
locking it. Sort of like an harmonic stick-slip. Even for pure control 
voltages or noise you might not want to have complete chaos, but some 
recognizable pattern. In other words some autocorrelation with a 
controllable length would be desirable.

> I believe 
> that the second work you referenced (same author) would allow
> voltage-controlled time scaling (e.g., V/Oct), since both the
> underlying quadrature oscillator and the driving pulse oscillator
> could be built using our usual OTA methods.

Yes, that's the idea - in fact the paper lists "circuit independent" 
structures for the realization of the proposed system, which means 
you're home almost free. You also seem to get some highly interesting 
pulse trains out of it.

> It isn't clear whether the VC in the first paper is used for time
> scaling or for changing the chaotic pattern.  Right now, I only have
> access to the abstracts.

It can do both, basically you have one divergent (quasi-harmonic) 
oscillator (implementable with OTA), a threshold comparator and a reset 
switch. The gm of the OTA and the threshold voltage all influence the 
behaviour. The more I look at it I think that both papers have quite a 
few things in common from a structural point of view. It's interesting 
to see them appear almost at the same time (and cite each others 
earlier works, which I have not yet studied). Both structures have 
potential for some serious circuit bending, even if you'd probably lose 
the ability to analyze them very soon.

> The system I am currently working with is based on the ideas of J. C.
> Sprott: <http://sprott.physics.wisc.edu/pubs/paper245.htm>  He has
> very kindly put the results of much of his research up at his site. 

I haven't had the time yet to delve deeper into his papers, but the link 
is in my bookmark file...

> I like his idea of using cascaded integrators, because you can think
> of the three outputs as a signal and its two successive derivatives. 

I guess you could just use that structure and inject a pulse train some 
strategic place as well.

>    (First experiments still up
> at  <http://home.earthlink.net/~ijfritz/xfer.htm>)

Speaking of which - how big are the MP3's? My modem is still recovering 
from the download of the page itself (I know, I should get DSL).


Achim.
-- 
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