Chua's oscillator circuit -- Intuitive picture

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I have been trying to understand intuitively why Chua's circuit should want to toggle between modes as it does.

The aim is to internalize this concept the way a Steve Mould or a 3Blue1Brown might help me do :smile:

Which is closer to the truth:
(A) Rectification of the signal around one bias point builds up a DC shift, which increasingly pushes towards another bias point, and vice versa
(B) Like an actively "de-damped" pendulum on top of a mini rocking chair, with the "rocking arcs" shaped so as to be metastable when vertical
 
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Swamp Thing said:
Which is closer to the truth:
How you conceptualise Chua's oscillator, will depend heavily upon your background, or the field from which your approach.
 
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Since chaos cannot be present without instabilities (e.g. a positive max Lyapunov exponent along the trajectories in the strange attractor) view (B) sounds more directly closer to the mathematical definition of chaos. On the other hand, (A) sort of describes a positive feedback mechanism that "spools up", so assuming that is how the electronics in Chua's circuit actually "work", then this may be just as valid as a practical description of the flipping between the two regions (I have ever only worked on the equations, never with the actual circuit, so I am biased towards the analysis of the equations).
 
As a radio engineer, it seems to me to resemble some behaviour which was well known by 1910. If we have two resonant circuits of the same frequency that are coupled together closely, then if we apply an initial impulse, damped oscillation will occur at one of two frequencies at random.
 
Baluncore said:
How you conceptualise Chua's oscillator, will depend heavily upon your background, or the field from which your approach.

Yes, I guess I was framing my question like, "Is a needle more like a burger or more like a soprano?" One could make a case for both by stretching each analogy enough. :smile:
 
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I am trying to relate charges on those two capacitors to the populations of Foxes and Rabbits in the first situation which was presented to me as chaotic.
 
Here is a simulation in LTspice using real electronic components.
Chua's circuit 3.webp
 

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Baluncore said:
real
Could you drop one of those on your foot? :wink:
 
sophiecentaur said:
Could you drop one of those on your foot?
Yes. Every component part is available commercially, so you can build it, and it will work. There are no tricks being performed by LTspice with controlled sources to synthesise Chua's diodes.

There are two attractors, at V2 = ±1.8 volts. As the signal is amplified by the local gain, the oscillator signal orbits that attractor, until the phasor reaches an amplitude where it can escape across the saddle near zero volts, to the other attractor. While crossing the saddle, the phasor is attenuated, whereupon the process is repeated, each time with a different escape velocity and attenuation. Notice how the first cycle of the phasor has a different amplitude each time, and that there are occasions when it fails to complete the saddle crossing.
Chua's circuit Osc.webp
 
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Baluncore said:
While crossing the saddle, the phasor is attenuated

Is the energy dissipated, or is the energy transferred to another element than the one whose voltage is plotted?
 
  • #12
Swamp Thing said:
Is the energy dissipated, or is the energy transferred to another element than the one whose voltage is plotted?
I am not sure. It may be dissipated in the linear resistor between the two capacitors, or it could be invested, regenerated in Chua's non-linear diode, which appears as a negative resistance amplifier, obviously with a power supply capable of absorbing energy.

To keep it conceptually simple, I did only plot the C2 component of the phasor. If you run the simulation, you can plot the power dissipated in the linear resistor.
 
  • #13
Baluncore said:
Yes. Every component part is available commercially, so you can build it, and it will work.
That's more of a philosophical idea - like treating any mathematical process as being a 'real' physical process. However accurate, a mathematical model is still not the real thing. I think that dodgy conclusions can be drawn too easily by having too much faith what a simulation actually does if yo are not totally confident that the simulator has not supplied hidden values to parameters that the user didn't supply. PF often receives posts with this problem.
Just being picky, I know but there should always be a caveat about this, particularly in fringe situations (chaos plus noise, for instance)
 
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sophiecentaur said:
However accurate, a mathematical model is still not the real thing.
Someone might want to build a real circuit. That schematic and simulation is the best help I can provide.

I believe it is the schematic and simulation of a physical circuit that worked, and that was then being shared. It will be somewhere in the LTspice archives.