# Chua's Circuit

- a simple electronic circuit, developed by
Leon Chua, showing chaotic
dynamics.

Simulation

Circuit

The applet shows a simulation of Chua's circuit, plotting the
voltage measured across *C1* against the voltage measured across
*C2*. This corresponds to the display on an *X-Y
*oscilloscope with probes connected across these capacitors. The
initial values of the parameters used in the applet correspond to the
component values in the circuit diagram, and show a simple periodic
orbit (oscillation). The transition to chaotic dynamics can be found
by *carefully* decreasing *R* or *C1*, (e.g. decrease
*R* in steps of 0.01 to 1.2K). The simulation compares well with
what is actually seen on an oscilloscope. Chaos seems to develop via
a subharmonic cascade.

If you do not have access to an oscilloscope, you can use the
voltage across *C1* or *C2* as the input to a high input
impedance audio amplifier (with the component values shown the
frequency of the oscillations is in the audio range). It turns out
that the ear is very sensitive to the development of a weak
subharmonic. The subharmonic becomes the fundamental an octave below
the original tone, and the ear hears the note drop an octave even
when the intensity of the new fundamental is very weak. The first two
or three transitions in the subharmonic cascade route to chaos, and
the onset of chaos (noise!) are very audible.

How the circuit works

Building the circuit

Why Chaos?

Circuit equations

Universality

Bibliography

Last modified Sunday, December 5, 1999

Michael Cross