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Lorenz's circuit.

Edward Norton Lorenz derived his equations from Saltzman's free convection equations,
simplified as to get the essence of the non-periodic behaviour noticed about their variations.
Written in 1962 and published in 1963, his original paper contains all the main characters
of the chaos theory - although this theory didn't exist at the time : the use of a computer,
simplifications of the equations, sensivity to initial conditions, use of Poincaré's map, etc ...

Original Lorenz paper - Deterministic nonperiodic flow (1963) - PDF

Lorenz equation set
dx / dt = α ( y - x ) 
dy / dt = -y + x ( γ - z ) 
dz / dt = xy - βz 
α = 10R1,R2
β = 8/3R7
γ = 28R3

The schema derives directly from the equations.
It uses 3 chips : one quad-AOP and two analog multipliers.

Time series of the XYZ outputs.
Note the flip over zero volt of both XY traces.

2D parametric plot of Z vs X attractor.
The starting point is located at zero volt and jumps
alternatively on the two sides of the attractor.

This FFT of the Z signal shows a maximum at 134 Hz.

Chaotic oscillators