Abstract
Hybrid analogue-digital computers have been shown to have certain advantages over traditional digital computers when solving nonlinear partial differential equations. Motivated by this fact, we implement the Lorenz equations on an analogue electronic computer and vary the parameters to analyze the bifurcations. With the working circuit, we compared experimental results to various digital simulations to assess the effectiveness of our circuit. We find clear qualitative agreement between the physical circuit and digital simulations; however, we observe a noticeable quantitative difference in behavior. The circuit depicts a picturesque Lorenz Butterfly plot and bifurcates into fixed points and chaos; however, these bifurcations occur at different r values than the theory predicts. Lastly, we built a noise generation circuit and observed the stochastic effects on the circuit.
Recommended Citation
LeFevre, Reed and Doyle, James
(2025)
"Making and Breaking Chaos: Analog Computer Implementation of the Lorenz Model,"
Macalester Journal of Physics and Astronomy: Vol. 13:
Iss.
1, Article 7.
Available at:
https://digitalcommons.macalester.edu/mjpa/vol13/iss1/7