Since the discovery of Giant Magnetoresistance in the late 80s, Spintronics has become an emerging field of electronics. One critical component to modern day wireless communications is the microwave voltage oscillator. This work explores the use of Spin Torque Nano Oscillators (STNOs) to produce a spintronics voltage oscillator in the microwave range. STNOs are quite small -- on the order of 10 nm -- and frequency agile. However, experimental results to date have produced power outputs that are too small to be useful. To increase power output, we investigate systems of coupled STNOs. Numerical simulations indicate that n synchronized STNOs configured in series or parallel produce n2-times as much power as n uncoupled STNOs. However as the number of oscillators n increases, the regions of parameter space corresponding to synchronization tend to shrink. To set the foundation for further analysis, we consider both Spherical and Complex Stereographic coordinates for the Landau-Lifshitz-Gilbert Equation with spin torque term. Both coordinate systems effectively reduce the equation of a single STNO from a three dimensions to two. Further, the Complex Stereographic representation transforms the equation into a nearly polynomial form that may prove useful for advanced dynamics analysis. Qualitative bifurcation diagrams show a rich set of behaviors in the parallel and series coupled systems and serve to develop intuition in system dynamics.
