Physics 427

Dr. Ayars

Kiers' circuit

This is an electronic circuit that simulates a very basic (minimal) self-driving chaotic equation. No external oscillator source is required, it just oscillates on its own. There is only one adjustable parameter in the equation, which is set by a digital potentiometer. This digital potentiometer is controlled by an Arduino microcontroller, which interfaces to a computer using SCPI-compatible commands. With SCPI commands, the computer user can set resistor values (0-1530) or generate automatic sweeps of resistor values, as well as query the Arduino to obtain current settings.

Depending on the resistor setting, the oscillator output can be stable... or not! Outputs for x, x-dot, and x-double-dot are available, so one can plot the equation trajectory in 3D phase space. Headphone output is available for x, so students can also listen to the output (it's in audio range) and hear bifurcations as secondary harmonics. Poincare plots are not available since there is no external reference drive signal, but one can plot return maps from the data. The circuit is reasonably fast (interesting things happen at 500-1000 Hz) so one can obtain enormous amounts of data with a DAQ card very easily. Interesting investigations could include mapping bifurcations, generating return maps, and determination of Lyapunov exponent at different drive parameters.

In addition, the circuit has an input. In theory, feeding a small amount of the x output of one circuit into the input of the second circuit, when the circuits are on the same resistor setting, should cause the two circuits to synchronize. This promises to be rather interesting, but has not been tested yet!

This circuit was developed by Eric Ayars, from a paper by Ken Kiers, Dory Schmidt, and J.C. Sprott. It works very reliably.

Picture of this apparatus

Here is the Schematic for this circuit.

Reading

Questions

Experiments