The scope of our study of chaotic phenomena looked beyond our common association of chaos with the condition of our respective dorm rooms. It turns out that the chaos in which we were interested was that which we observed as the output of our circuit. If the input frequency or voltage amplitude was varied, it could be observed that at certain values, the output would behave unexpectedly.
A system can be described as chaotic if changes in its initial values or parameters result in unpredictable outcomes. A phrase often used in the context of chaos is the 'Butterfly Effect' which considers valid the idea that a butterfly's flight on one side of the world can affect the weather patterns on the other and make them unpredictable.
Any system described as chaotic must exhibit non-linear properties. This means that if the input signal is periodic, the output of the system will be periodic. For a non-linear system, if the input is periodic, the output is not necessarily periodic. It can be periodic, but can also be sub-harmonic and chaotic. To take data for the observation of chaos, you need to vary a parameter of the input signal.
To identify chaos within a system, note observations such as sensitivity to changes in initial conditions. Also a Fourier analysis of the output of the system should reveal a broad spectrum of frequencies composing the output. Furthermore, you might notice increasing complexity of the system's motions as parameters are changed (for instance, period doubling may result, or a period of greater complexity). Other characteristics to identify chaos are noticing 'fractal properties' of the motion in phase space (measured by Poincaré maps) and the presence of transient chaotic motions - initial random-like motion that settles down into a regular motion (Moon pp 48-49).
Have a look again at our circuit. When the diode is forward biased, i.e. conducting, it acts as a constant voltage source. When it is reverse biased, however, it acts as a capacitor. The diode is not a perfect device and therefore experiences a non-zero time length for switching from forward to reverse bias and vice-versa. The amount of current through the diode affects the time it takes the diode to return to one of its bias equilibrium states. The greater the magnitude of the current, the more significant is this effect. Furthermore, as the diode acts as a capacitor, its impedance depends on frequency. If the amplitude of the input voltage is held constant, but the input's frequency changes, period doubling and chaos can also be observed.
Non-linearity in the system is present as a result of uncombined charges which crossed the diode's p-n junction while it was in the forward bias mode. When the diode switches to its reverse mode, these charges diffuse back over some amount of time. Therefore, the diode conducts for a short time after it switches from forward to reverse bias. If this 'short' time is significant relative to the input signal's period, then chaotic behavior may occur.
So, in our circuit, each cycle is composed of a conducting and non-conducting mode. As the magnitude of the current increases (or the input frequency changes) we might observe period doubling. Here the magnitude of the current during its (n+1)st cycle depends on that in the nth cycle: |Imax|n+1 = F(|Imax|n).
The circuit has an inherent resonant frequency: 
(occurs when the impedance of the
inductor = the impedance of the diode when it behaves like a capacitor). If the
input signal's frequency is close to this resonant frequency, then as the output's
amplitude increases, the diode voltage undergoes period doubling and eventually chaos.
This was found in our circuit as well as through modeling the system with MicroSim
Pspice.