We report a systematic investigation of the magnetic anisotropy effectsobserved in the deterministic spin dynamics of a magnetic particle in thepresence of a time-dependent magnetic field.The system is modeled by the Landau-Lifshitz-Gilbert equation and themagnetic field consists of two terms,a constant term and a term involving a harmonic time modulation.We consider a general quadratic anisotropic energy with three differentpreferential axes.The dynamical behavior of the system is represented in Lyapunov phase diagrams,and by calculating bifurcation diagrams, Poincaré sections andFourier spectra.We find an intricate distribution of shrimp-shaped regular island embeddedin wide chaotic phases.Anisotropy effects are found to play a key role in defining the symmetriesof regular and chaotic stability phases.