Nonlinear dynamics of a spherical magnetic particle and an ensemble of such particles in an external oscillating magnetic field have been studied analytically and numerically in terms of the Landau-Lifshitz-Gilbert equation. The exact analytical formulas have been obtained allowing the calculation of the projections of the mean-in-time magnetization of the system on the frequency of an external field and initial orientation of magnetic moments. The behavior of the system in the limiting cases of low and high frequencies has been considered. The analytical solutions obtained agree well with the direct numerical calculations of the Landau-Lifshitz-Gilbert equation. The analytical theory of the effect of the nonlinear dynamic polarization has been developed, and its applicability for designing devises of magnetic memory has been discussed.
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