For ferroelectric systems described by an ng1 polar vector order parameter p, a new term in the free-energy density, \ensuremath{\beta}${[\mathrm{p}}^{2}$\ensuremath{\nabla}\ensuremath{\cdot}p-p\ensuremath{\cdot}\ensuremath{\nabla}${(\mathrm{p}}^{2}$)], is allowed. Considering an isotropic, centrosymmetric model and using Landau theory, we show that as a result the ferroelectric phase becomes locally unstable when \ensuremath{\Vert}\ensuremath{\beta}\ensuremath{\Vert} is sufficiently large. For \ensuremath{\Vert}\ensuremath{\beta}\ensuremath{\Vert} values above the critical one, the ordered phase has a modulated antiferroelectric structure. Several alternative structures are considered, and it is argued that for n=3 the most likely phase is a cubic one (space group ${O}_{h}^{9}$). Immediately above the critical value of \ensuremath{\Vert}\ensuremath{\beta}\ensuremath{\Vert}, the transition to the ordered phase is of second order. When \ensuremath{\Vert}\ensuremath{\beta}\ensuremath{\Vert} is further increased, a tricritical point is reached above which the transition is first order. The effect of fluctuations on the above results is analyzed by using renormalization-group theory and expanding to O(\ensuremath{\epsilon}) in 4-\ensuremath{\epsilon} dimensions. The new term is found to be relevant when n${n}_{0}$=4-11\ensuremath{\epsilon}/4+O(${\ensuremath{\epsilon}}^{2}$), in which case no stable fixed points exist for 1.86\ensuremath{\lesssim}n${n}_{0}$. Thus ferroelectrics and ferromagnets are not necessarily in the same universality class. An examination of the renormalization-group flows, together with the results of the classical Landau analysis, indicates that modulated structures are possible immediately below the order-disorder transition regardless of the magnitude of \ensuremath{\beta}(\ensuremath{\ne}0). Some experimental data which appear to agree with the theoretical results are discussed.