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In this work, we characterize the magnetization dynamics of an anisotropic magnetic particle under the presence of external magnetic fields. The temporal evolution is described by the Landau-Lifshitz-Gilbert equation. The anisotropy is assumed uniaxial, whereas the external magnetic fields are composed by a homogenous and a time-dependent one. We analyze the case of a periodic and a quasi-periodic time driven dependent field. Different indicators are used to detect the dynamical behaviors, such as Lyapunov exponent and Fourier power spectrum. We show that for both periodic and quasi-periodic driven fields the system exhibits chaotic and regular states. We perform an intensive analysis from the parametric point of view, since we vary simultaneously two parameters when the largest Lyapunov exponent is calculated. Finally, we found that there are other states called strange non-chaotic attractors. [ABSTRACT FROM AUTHOR]