Chua chaos circuit

[Fenichel]

  I have been playing with a Chua chaos circuit (see Chua circuit.pdf attachment).  The PCB works (see chaos YT.jpg attachment), but (as I'd been warned) the beautiful strange-attractor pattern (see http://en.wikipedia.org/wiki/Chua%27s_circuit) doesn't appear on my digital scope (see the chaos XY.jpg attachment).  Is there some circuitry that can be put in between the Chua circuit and the probes to trick the digital scope into -- for this limited purpose -- behaving like an analog one?

  Incidentally, I have 2 spare PCBs of the circuit, if anyone wants them.

[ivaylo]

Can't make the Rigol analog, but you can export the data from the two channels and visualize any way you want in you favorite software on a PC.

I'd love a PCB of this if you still have extras...

[peter.mcnair]

Although I know nothing about modern scopes, I would like something similar: essentially a digital storage oscilloscope which has storage facility when operating in XY-mode. I too am interested in chaotic attractors: (http://analog-ontology.blogspot.co.uk/2015/02/bessel-attractors.html)
and currently obtain output using an XY plotter (pen and paper) or analog scope plus a digital camera with (e.g. a 2 second exposure).

[Fenichel]

Can't make the Rigol analog, but you can export the data from the two channels and visualize any way you want in you favorite software on a PC.

  I will try that, but the visualization feedback loop might then be uselessly long.  Until one sees the right pattern, one has no way of knowing whether the pots have been tweaked into the magic settings.

[ivaylo]

The other thing is your cluster is too tiny to see anything (at least what the second image shows). Can you center it in the XY plot and make it bigger ("zoom in")? Then make sure the scope is not plotting dots only, but lines (or "vectors", not sure how Rigol calls that). Also if the signal is too long can't you start/stop the acquisition so the plot doesn't get crowded (and that's one advantage of I what I suggested above - on a PC you can control how much you are plotting/discarding).

[Fenichel]

The other thing is your cluster is too tiny to see anything (at least what the second image shows). Can you center it in the XY plot and make it bigger ("zoom in")? Then make sure the scope is not plotting dots only, but lines (or "vectors", not sure how Rigol calls that). Also if the signal is too long can't you start/stop the acquisition so the plot doesn't get crowded (and that's one advantage of I what I suggested above - on a PC you can control how much you are plotting/discarding).

No, the format of the XY view on my scope is, as far as I can tell, fixed.  It's probably fine for looking at Lissajous figures; looking for strange attractors is rather a niche app.  Rigol does have a dots/vectors toggle, but it doesn't help for XY.  I can make the signal sparser by sampling it in bursts, but that doesn't seem to help either.  What I need is the analog-scope effect of watching the screen change as I fiddle with the pots. 

[T3sl4co1l]

Well, the scales are all wrong, there's your problem...  Why not use AC input coupling??

Also, is the signal of interest really that damn fast?  Surely you should be using much longer time constants so you can actually see it evolving.  Up at 100MHz, you wouldn't see anything more than a blur on an analog scope either!

Tim

[Fenichel]

Well, the scales are all wrong, there's your problem...  Why not use AC input coupling??

  Thanks for reminding me about AC input coupling.  I am such a newby that I don't often think of it.  AC input coupling makes the X-Y-Z signals easier to find, and I should use AC coupling more often.  Unfortunately, AC input coupling doesn't improve the XY plot; it is still an unstable dot cloud. 

Also, is the signal of interest really that damn fast?  Surely you should be using much longer time constants so you can actually see it evolving.  Up at 100MHz, you wouldn't see anything more than a blur on an analog scope either!

  I am going to go back to a breadboard version of the circuit, and there use larger resistors & capacitors, thereby lengthening the quasiperiods of the oscillators.  From what I've seen in Web descriptions of the circuit,

• the component values I've used have been used by others, with good results, but
  
• those good results have appeared only on analog scopes.

so I am not optimistic about seeing the attractor on my DSO.  Still, a slower version of the circuit may make it realistic to pipe the circuit's waveforms into my computer, and to manipulate the XY data there.

[tggzzz]

XY plots are notoriously tricky on DSOs, so much so that some use it to demonstrate that analogue scopes are better!

If you have access to an analogue scope, you might like to use it on your circuit.

[Fenichel]

  The behavior of this circuit is relatively unaffected by moderate (1 to 2 orders of magnitude) changes in the R & C component values.  Big increases of the RC time constants do not much change the primary quasiperiods of the 3 oscillators (they stay ~5 ns), but those changes introduce longer quasiperiods (say, 300 ns) that are modulated, more or less, by the old 5-ns signal.
  I'm going to try to borrow an analog scope for this.

[Fenichel]

  On an borrowed analog oscilloscope in XY mode, the circuit with the component values I originally specified does what it should, demonstrating a variety of beautiful strange attractors.  It almost tempts me to get an analog scope.

[GK]

I bet mine are better than yours   

http://www.glensstuff.com/sprottsystems/sprottsystems.htm

[nuno]

Very interesting. It's way out of my league, but an unijunction transistor has a range of negative resistance; would it be possible to use it as Chua's diode?

[Fenichel]

I bet mine are better than yours   

http://www.glensstuff.com/sprottsystems/sprottsystems.htm

  Yes, yours are better.  With only the circuit I described in the OP, I get a limited range of attractors.  This is the first post of 2.

[Fenichel]

  More attractors.

[GK]

You have found a couple of periodic windows. It can be fun to see if you can alter a coefficient/constant finely enough to observe intermittency when enterning a periodic window:




Published on Sep 2, 2014


Chaotic Sprott System case S:

dx/dt = -x-4y
dy/dt = x+z^2
dz/dt = 1+x

A variable DC potential is summed with the z^2 term of the y equation, to control the system state from periodic to chaotic. The period-3 window is sufficiently wide to briefly visibly appear (with some careful control) at the 23 second point. Intermittency is observable beforehand. The strange attractor is eventually destroyed in an identity crisis.

2D plane view, x state on the horizontal axis, y state on the vertical.

[Fenichel]

  I have got back to this, with limited success, but the results may be of interest to some.  The results are described on my Web site at http://www.fenichel.net/pages/Indoor_Activities/electronics/chaos/chaos.htm

[GK]

Nice to see someone else play around with these chaos and trigonometric transformation circuits. This stuff doesn't seem to attract a lot of interest.

I did play around on bread board with an all-analogue transformation unit/rotator very similar to your circuit, though I used a state variable oscillator to generate the reference sine and cosines. The SVO provides these signals implicitly. However I didn't progress any further with the design mostly due to having too many other projects on the go and a fundamental limitation of a simple implementation of a SVO built to operate at very low frequencies. I wanted a variable-frequency reference oscillator to cover the range of 0.1 to a couple of Hz. The problem with a "pure" oscillator rather than function generation techniques is that invariably some kind of amplitude stabilization is required. If your oscillator operates at a period down to 10 seconds and takes, say, just for example, 50 cycles to stabilize in amplitude, then you can go off and make yourself a cup of instant coffee with each moderate tweak of the frequency control knob, while your 'scope display wobbles itself back to equilibrium.

BTW, you can compress you video files down in size considerably with Any Video Convertor:
http://www.any-video-converter.com/

         

[tautech]

Nice to see someone else play around with these chaos and trigonometric transformation circuits. This stuff doesn't seem to attract a lot of interest.

Sure it's not everybodies cup of tea, but they are fascinating IMO.
Glen, I often check back through your posts just to ensure I have not missed any of your wonderful creations.
Please keep "showing off" your work. 

[GK]

I often check back through your posts just to ensure I have not missed any of your wonderful creations.

Ooh, a stalker. Are you female and pretty?