The Duffing oscillator: A precise electronic analog chaos demonstrator for the undergraduate laboratory

A simple electronic circuit is described which can be used in the student laboratory to demonstrate and study nonlinear effects and chaos. The circuit shows the changes to the dynamical properties of the system with respect to three control parameters: the applied voltage amplitude and frequency and the circuit damping. The response voltage and its derivative can be displayed to give the phase space plot and the bifurcation diagram against any control parameter. The circuit is sufficiently ideal and stable to allow comparison of its analog output with the output obtained from standard digital computer simulations. As examples, the routes to chaos with respect to the control parameters and the bifurcation route to chaos, which follows the Feigenbaum scenario, are shown