A Nonlinear Electrical Circuit Exhibiting Period Doubling Bifurcation and Chaotic Behavior

By constructing a circuit consisting of a diode, resistor, and inductor in series with sinusoidallydriven function generator, period doubling bifurcation and chaotic behavior were observed in this experiment. By using a fixed frequency close to the value of resonance frequency of the circuit and adjusting the voltage amplitude of the function generator, the circuit exhibited chaotic behavior. A bifurcation diagram of the data was created at a fixed frequency of 376 kHz to illustrate the period doubling route to chaos that the circuit experienced as the function generator’s voltage increased. Two trials where the voltage of the function generator and across the diode were recorded were taken at two different fixed frequencies: 276 kHz and 376 kHz. Determining where at least three period doubling bifurcation points occurred in each trial allowed for the calculations of the Feigenbaum constant, δ = 4.669, for each trial. For the 276 kHz fixed frequency δ = 4.1±0.7 and for the 376 kHz fixed frequency δ = 4.0±0.7, which is 13% and 14% difference from the accepted value respectively.