The following diagrams are oscilloscope readings of our output voltage at different input frequencies. It is evident from the data that as the input frequency is increased from resonance the output or diode voltage is seen to undergo period doubling, quadrupling, octupling and eventually becomes chaotic. If we continue to increase the input frequency the diode voltage is then seen to escape the region of chaotic behavior, descend through period octupling, quadrupling, doubling and finally returns to the normal periodicity that was exhibited at resonance.
Using 
, we were able to find a value for the capacitance of the diode in its reverse
bias mode. In our experiment we observed that the output across the diode was a
maximum when the input frequency was about 5.5 kHz (resonance). Since our inductor
had an inductance of 25 mH, we calculated the capacitance of the diode to be 33.49 nF.
Although in this experiment we chose to vary the frequency of the input instead of the voltage, we also observed that changes in the amplitude of the input signal could lead to period doubling and chaos. Unfortunately the resonating frequency of our circuit produced quite a bit of noise, as demonstrated in the above diagram. So when we decided to try varying the input voltage we chose an input frequency of 140.8 kHz which produced a lot less noise. At an amplitude of 2 V the output voltage was observed to have period octupling. When the amplitude was increased to 4.1 V the voltage output of the circuit first exhibited chaotic behavior and then returned to period octupling. At an amplitude of 4.9 V, the voltage output demonstrated period quadrupling while at 6 V the voltage output showed period doubling. At greater amplitudes the output voltage returned to normal periodicity. While this is not a complete examination of the consequences of varying the amplitude of the input, it confirms the notion that as long as one parameter of the input is varied an oscillatory system will exhibit period doubling and chaotic behavior.
Check out more visualizations of the dynamics of our system including phase spaces, Poincare Sections, Fourier analysis and bifurcation diagrams.