Coupled perturbed heteroclinic cycles: Synchronization and dynamical behaviors of spin-torque oscillators

Following our Rapid Communication, we present a more detailed analysis of the synchronization of spin-torque oscillators (STOs), as well as some other nonlinear characteristics of STO, by using the perturbed heteroclinic cycle model rather than a linear phase oscillator model. We analyze four critical points of the system and numerically get the fifth one and meanwhile systematically study the bifurcation process of the system. Three of the fixed points limit the parameter regions for sustaining an oscillation, and another one is the boundary between a global oscillation (out-of-plane mode oscillation) and a local oscillation (in-plane mode oscillation). The frequency of the physically more relevant global oscillation is also estimated depending on the system parameters. The results are not only significant for the design of useful devices but also important for further understanding the response of an STO to an external signal and interpreting the difficulty of synchronizing serially connected STOs. We also discuss in detail several other synchronization schemes.