When current travels through a spin torque oscillator, a spin torque not only acts on the oscillating free layer, but the hard polarizing layer as well. This provides the type of non-linear feedback which enables chaos to arise. By numerically integrating the modified Landau Lifshitz equation (with spin torque term), we can simulate the dynamical motion of spin torque oscillators. This project's objectives is to use numerical simulations to study the effects of various parameters such as the Gilbert damping constant on the transitions of the oscillator from periodic to quasiperiodic to chaotic motion. Goals include quantifying the chaoticity of the motion, determining which regions of the parameter space preclude chaos, and analyzing the behavior of a 2 free-layer spin torque system in particular. Applications of this research include getting rid of unwanted chaos in spin torque oscillators and boosting the coherence and strength of the emitted microwaves for various spin torque systems.