Chua's circuit

[1] 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".

[2] An autonomous circuit made from standard components (resistors, capacitors, inductors) must satisfy three criteria before it can display chaotic behaviour.

[6] A self-excited chaotic attractor, known as "the double scroll" because of its shape in the (x, y, z) space, was first observed in a circuit containing a nonlinear element such that f(x) was a 3-segment piecewise-linear function.

[8] The classical implementation of Chua circuit is switched on at the zero initial data, thus a conjecture was that the chaotic behavior is possible only in the case of unstable zero equilibrium.

[5] In this case a chaotic attractor in mathematical model can be obtained numerically, with relative ease, by standard computational procedure where after transient process a trajectory, started from a point of unstable manifold in a small neighborhood of unstable zero equilibrium, reaches and computes a self-excited attractor.

[13] First confirmation of hidden chaos was reported in 2022 at the Theoretical Nonlinear Dynamics Lab at the Institute of Radio-engineering and Electronics of the Russian Academy of Sciences.

One version of Chua's circuit, where the nonlinear Chua's diode is synthesized by an op amp negative impedance converter (OPA1) and a diode–resistor network (D1, D2, both R2)
Computer simulation of Chua's circuit after 100 seconds, showing chaotic "double scroll" attractor pattern
Chua's attractor
Chua's attractor for different values of the α parameter
Two hidden chaotic attractors and one hidden periodic attractor coexist with two trivial attractors in Chua circuit (from the IJBC cover [ 9 ] ).