Neutron stars are the remnants of supernova explosions, and harbor the densest matter found in the universe. Because of their extreme physical characteristics, neutron stars make superb laboratories from which to study the nature of matter under conditions of extreme density that are not reproducible on Earth. The understanding of QCD matter is of fundamental importance to modern physics, and neutron stars provide a means of probing into the cold, dense region of the QCD phase diagram. Isolated pulsars are rotating neutron stars that emit beams of electromagnetic radiation into space which appear like lighthouses to observers on Earth. Observations of these objects have been documented with very high accuracy. Measurements of pulsar rotational velocity, along with its first and second time derivatives, show that they slow down over time. The generally accepted explanation for the spin-down is that the pulsars behave like giant magnetic dipoles that lose energy in the form of electromagnetic radiation. This assumption of magnetic dipole radiation (MDR) leads to a general power law constructed from observation and governed by the braking index n, which relates the frequency to spin-down. The theoretical value for n is exactly 3 for MDR, but accurate observational measurements consistently yield values between 1.0 and 2.8. The goal of this thesis is to improve understanding of the braking index through a two pronged investigation into this important quantity. We develop a frequency dependent model of the braking index that allows changing moment of inertia of the star, and changes in magnetic field properties in the MDR torque mechanism. For the first time, we use physically realistic equations of state, along with state of the art computational codes to determine the dynamic neutron star properties required. We probe the stars at constant baryonic rest masses ranging from 1.0 to 2.2 solar masses over a range of frequency spanning from zero to the Kepler frequency for each star. We also develop a toy model of two interacting dipoles to make a first attempt at describing a plausible scenario by which the pulsar magnetic moment may evolve in time.