  In magnetic films driven by spin-polarized currents, the
perpendicular-to-plane anisotropy is equivalent to breaking the time
translation symmetry, i.e., to a parametric pumping. In this work, we
numerically study those current-driven magnets via the
Landau-Lifshitz-Gilbert-Slonczewski equation in one spatial dimension. We
consider a space-dependent anisotropy field in the parametric-like regime. The
anisotropy profile is antisymmetric to the middle point of the system. We find
several dissipative states and dynamical behavior and focus on localized
patterns that undergo oscillatory and phase instabilities. Using numerical
simulations, we characterize the localized states' bifurcations and present the
corresponding diagram of phases.
