| Over the past few years, it has been shown, through theory and experiments, that the AC current produced by spin torque nano-oscillators (STNO), coupled in an array, can lead to feedback between the STNOs causing them to synchronize. Once synchronized the microwave power output of an array is significantly larger than that of an individual valve. It has also been observed that in coupling STNOs into arrays, the region of parameter space that corresponds to synchronization between the individual oscillators tends to shrink. In order to explore the parameter space and find regions of synchronization, Complex Stereographic coordinates for the governing equations are employed, reducing the dimensions of a single STNO from three dimensions to two. Then, numerical computations are used to explore the dynamics of the coupled arrays of STNOs and to generate bifurcation diagrams for locating regions of synchronization. Once these regions are discovered, the Transverse Lyapunov Exponents of the synchronized system are calculated to determine whether the synchronization between the oscillators is stable. We show that for certain values of the parameters, mainly the injected current and the angle of the applied field, there are regions where synchronization is easier to obtain. |
