Nonlinear magnetization oscillations in small cylindrical ferromagnetic particles

Radial-symmetric nonlinear magnetization oscillations are considered for small ferromagnetic cylindrical particles both for free and fixed boundary conditions on a lateral side of the particles. It turns out that even for nonlinear oscillations of small amplitude the relation between frequency and amplitude is complex enough and comprises a bifurcations series. The oscillation character depends essentially on boundary conditions, for example, for free boundary conditions there are bifurcations of solutions, whereas in the case of fixed conditions such bifurcations are absent. The possibilities of generalization of the results obtained to the cases of oscillations in a cylinder with a more complex angular dependence and radial-symmetric oscillations in a sphere particle are discussed