The influence of the shape parameter (oblateness) of a uniaxial ellipsoidal nanoparticle on the dynamics of its magnetic moment upon magnetization along the symmetry axis and excitation by a weak transverse high-frequency field in the region of parameters where the equilibrium magnetic moment of the nanoparticle and the external static field is noncollinear has been studied. It is shown that as the oblateness increases, the irregularity of the oscillations increases, which at first affects only their amplitude, but then also the time dependence. The intervals of the shape parameter (or frequency), where various nonlinear modes of precession are realized - dynamic bistability, complex spatial attractors and chaos, were revealed using bifurcation diagrams.