I'm working on chaotic signals and I was wondering if anyone here is an expert on the subject. I've already built a circuit based on the Arneodo system (attachment 1) but getting chaos out of it is getting on my nerves. It takes about 1 hour for the circuit work (Don't know why. Maybe the ICs need to heat up first?) and when it does work it always has to start at period 1 (stable oscillation), then period 2 and 3 (oscillations with 2 and 3 highs and lows respectively), then finally I get chaos (wild unpredictable oscillations) at period 4 (attachment 2). I was wondering if there is a circuit out there that can give me a chaotic signal (period 4) as soon as I turn on the power supply. I'm already considering building the circuit by J.C. Sprott.
I realize a lot of wild math is involved but electronically it is really simple (and FUN!).
More questions and developments(?) to come

 

Any circuit which "solves" a set of linear differential equations that exhibit chaotic behavior will produce similar results. Examples would be the Lorentz or the Rössler systems. There is an excellent book by Strogatz, S.,Nonlinear Dynamics and Chaos, Ch.9-12 which has solid theory and interesting examples.

 

As far as I remember, such system has a parameter which determines the "degree of chaos", and this behavior can be the case where this parameter slowly changes from the stable side to the chaotic side.

Have you ever played with a mandelbrot set? The color of the points is computed from the time it takes for the point to "escape" some value, and for some points it takes longer than for others. Your case can be similar, the system seems to be stable for a while, but then ends in chaos anyway.

 

As far as I remember, such system has a parameter which determines the "degree of chaos", and this behavior can be the case where this parameter slowly changes from the stable side to the chaotic side.

Yup, the potentiometer R4 in the non-linear circuit determines those periods. Chaos (the kind I'm satisfied with anyway) starts at around 7.2KΩ but when I turn the supply off and back on again the chaos disappears. Come to think of it, it also disappeared when some dude smashed his knee on the table I was working on. The supply was never interrupted and no connections were broken - the signal just winked out of existence right in front of me. If it takes way too long for chaos to begin, then this system won't do for what I have in mind. And I haven't played around with a Mandelbrot set.

@Papabravo:
Stephen Strogatz rocks!!! I have his entire "Chaos for dummies" lecture but I still can't wrap my head around all the "wild math" that other people use to explain chaos. Anyway, I kinda built JC Sprott's Chaos generator while waiting for my Arneodo system to work (patience is not one of strong points)

Thanks for the quick reply guys. I'll post simulation results for the second generator. I'm gonna try to get these things to "synchonize".