In the present work, we study the dynamics of a magnetic nanoparticle coupled through the magnetoelectric coupling to the ferroelectric crystal. The model of our interest is nonlinear, and we explore the problem under different limits of weak and strong linearity. By applying two electric fields with different frequencies, we control the form of the confinement potential of the ferroelectric subsystem and realize different types of dynamics. We proved that the system is more sensitive to magnetoelectric coupling in the case of double-well potential. In particular, in the case of strong nonlinearity, arbitrary small values of magnetoelectric coupling lead to chaotic dynamics. In essence, magnetoelectric coupling plays a role akin to the small perturbations destroying invariant tors according to the KAM theorem. We showed that bifurcations in the system are of Hopf's type. We observed the formation of magnetoelectric fractals in the system. In the limit of weak nonlinearity, we studied a problem of parametric nonlinear resonance and enhancement of magnetic oscillations through magnetoelectric coupling.