Normally to observe chaotic behavior in the system of a Diode-Inductance Circuit the applied voltage would be varied while the input frequency would be maintained close to that of the resonating frequency of the inductor and the reverse capacitance of the diode. However, in our experiment we arbitrarily chose to demonstrate period doubling and chaotic behavior by varying the input frequency instead of the voltage. In order to observe chaotic behavior in an oscillatory system one needs only to vary one parameter of the input or driving force, so while our methods are unconventional they still produce the desired results.
The phase spaces from the data page and those below are useful in that they provide information about the dynamics of our system at specific values of the input frequency. The Poincare Sections are a means of simplifying the phase space and demonstrate more clearly each stage of the transition from single periodicity to chaos in our system. The Fourier Transformations illustrate the predominant frequencies that compose our output voltages. Sometimes though it is helpful to get a more global view of the dynamics of a system by examining the entire range of a parameter at once, thereby allowing simultaneous comparison of periodic and chaotic behavior. The bifurcation diagram is an excellent method of presenting this overview and provides a summary of the essential dynamics of our system.
The following are phase portraits as plotted on the oscilloscope:
Period doubling at 156.2
kHz 
Period quadrupling at 128 kHz 
Chaos at 107.4 kHz
Periodicity: single double quadruple octuple chaos octuple quadruple double single
Frequency: 16 kHz 32 kHz 57 kHz 61 kHz 111 kHz 124 kHz 130 kHz 149 kHz 177 kHz