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].
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