Sprott discussed his search for the algebraically
simplest system of autonomous ordinary differential equations that
exhibits chaos. He described two systems, one with a quadratic
nonlinearity and one with an absolute value nonlinearity that are
simpler than the Lorenz and Roessler examples. He argued that
these are probably the simplest possible such cases. These systems
can be represented by a "jerk" function (a third derivative of the
scalar variable) and a single parameter.
The piecewise linear system is especially suitable for
electronic implementation using only diodes, resistors,
capacitors, and operational amplifiers. He demonstrated a simple
circuit that solves the equations in real-time, producing
period-doubling bifurcations and chaos in an audible signal. He
showed other variants of the chaotic circuit using even fewer
components.
