  In this paper, the voltage fluctuations of the Bonhoeffer van der pol
oscillator system with a non-ideal capacitor were investigated. Here, the
capacitor was modeled, using a fractional differential equation in which the
order of the fractional derivative is also a measure of the memory in the
dielectric. The governing fractional differential equation was derived using
two methods, namely a differential and integral approach. The former method
utilized a hierarchical resistor-capacitor (RC) ladder model while the latter
utilized the theory of the universal dielectric-response. The dynamical
behavior of the potential across the capacitor was found to be affected by this
parameter, and, therefore, the memory of the system. Additionally, findings
indicate that an increase in the memory parameter was associated with an
increase in the energy stored in the dielectric. It was found that oscillation
death resulted in a higher amount of stored energy in the dielectric over time,
as compared to behavior, which displayed relaxation oscillations or chaotic
fluctuations. The relatively-lower stored energy resulting from the latter
types of dynamical behavior appeared to be a consequence of the memory effect,
where present accumulations of energy in the capacitor are affected by previous
decreases in the potential. Hence, in this type of scenario, the dielectric
material can be thought of as remembering the past behavior of the voltage,
which leads to either a decrease, or an enhancement in the stored energy. The
non-ideal capacitor was also found to have a transitory nature, where it
behaves more like a resistor as {\alpha} approaches 0, and conversely, more
like a capacitor as {\alpha} goes to 1. Here, a decrease in {\alpha} was linked
to an enhanced metallic character of the dielectric.
