  Spontaneous pattern formation in a variety of spatially extended nonlinear
system always occurs through a modulation instability: homogeneous state of the
system becomes unstable with respect to growing modulation modes. Therefore,
the manipulation of the modulation instability is of primary importance in
controlling and manipulating the character of spatial patterns initiated by
that instability. We show that the spatio-temporal periodic modulation of the
potential of the spatially extended system results in a modification of its
pattern forming instability. Depending on the modulation character the
instability can be partially suppressed, can change its spectrum (for instance
the long wave instability can transform into short wave instability), can split
into two, or can be completely eliminated. The latter result is of especial
practical interest, as can be used to stabilize the intrinsically unstable
system. The result bears general character, as it is shown here on a universal
model of Complex Ginzburg-Landau equations in one and two spatial dimension
(and time). The physical mechanism of instability suppression can be applied to
a variety of intrinsically unstable dissipative systems, like self-focusing
lasers, reaction-diffusion systems, as well as in unstable conservative
systems, like attractive Bose Einstein condensates.
