Description

Chua's circuit is a simple electronic circuit that exhibits classic chaotic behavior. It produces an oscillating waveform that never repeats. The ease of construction of the circuit has made it a ubiquitous real-world example of a chaotic system, leading some to declare it "a paradigm for chaos" ¹.

From Wikipedia.

The code at chua.jl models the Chua circuit using ModelingToolkit.jl and the convenient ModelingToolkitStandardLibrary.jl, and, more specifically, its Electrical components.

In order to get this chaotic behavior, we need to satisfy a couple requirements.

We need at least one nonlinear element if you look at the diagram above, and that's what $N_R$ stands for, our nonlinear resistor. We need at least one locally active resistor, which is also $N_R$ in the diagram. Then, we need at least three energy storage elements, so that's where the capacitors $C_1$ and $C_2$ and the inductor $L$ come into play. That diagram is what we're going to be building. This is the resulting output according to the sims on the model that we've built:

Footnotes

1. Madan, R. N. (Ed.). (1993). Chua's circuit: a paradigm for chaos (Vol. 1). World Scientific. ↩