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Rossler's circuit.



Otto E Rossler designed his equations as a simplification of Lorenz's while keeping their essential chaotic behaviour.
Althought the shape of the attractor is simpler, it is chaotic and fractal, and has some link with the Moebius strip.

Original Rossler paper - An equation for continuous chaos (1976) - PDF




Rossler equation set
dx / dt = -y - z 
dy / dt = x + αy 
dz / dt = β + z(x - γ) 
ParametersComponents
α = 0.2R5,R7
β = 0.2R8,R9,R10
γ = 5.7R8,R9,R10





The schema closely follows the equations.
It uses two chips : one quad-AOP and one analog multiplier.















Time series of the XYZ outputs.
Note the quasi-orthogonality of both XY,
and the sudden shooting of the Z signal.















Parametric plot of Y vs X attractor.
The point starts at zero volt and follows an open spiral :
note how its trajectory is folded back onto itself.















This FFT of the X signal shows a maximum at 168 Hz,
close to the cutoff frequency given by 10 KΩ and 100 nF.











Chaotic oscillators