  We study theoretically the multiferroic dynamics in a composite
one-dimensional system consisting of BaTiO3 multiferroically coupled to an iron
chain. The method treats the magnetization and the polarization as
thermodynamic quantities describable via a combination of the Landau-Lifshits-
Gilbert and the Ginzburg-Landau dynamics coupled via an additional term in the
total free energy density. This term stems from the multiferroic interaction at
the interface. For a wide range of strengths of this coupling we predict the
possibility of obtaining a well-developed hysteresis in the ferromagnetic part
of the system induced by an external electric field. The dependence of the
reversal modes on the electric field frequency is also investigated and we
predict a considerable stability of the magnetization reversal for frequencies
in the range of 0.5 - 12 [GHz].
