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