In this report we study the Aizawa field by first computing a Taylor series expansion for the solution of an initial value problem. We then look for singularities (equilibrium points) of the field and plot the set of solutions which lie in the linear subspace spanned by the eigenvectors. Finally, we use the Parameterization Method to compute one and two dimensional stable and unstable manifolds of equilibria for the system. / Includes bibliography. / Thesis (M.S.)--Florida Atlantic University, 2018. / FAU Electronic Theses and Dissertations Collection