  We have investigated orthorhombic $R$MnO$_{3}$ ($R$=(Gd$_{1-y}$Tb$_{y}$))
crystals near the phase boundary between the paraelectric
$A$-type-antiferromagnetic (AF) phase (PA) and the ferroelectric
transverse-spiral-AF one (FS). The spiral AF structure breaks inversion
symmetry and induces the ferroelectric polarization through the inverse
Dzyaloshinskii-Moriya (DM) interaction. We have found that the PA-FS phase
boundary is located at around 0.15$<$$y$$<$0.2. In $y$=0.15 compound, PA and FS
phases appear in cooling scan, while FS is not observed in warming scan. This
result suggests that FS observed in $y$=0.15 is a metastable state arising from
the competition between PA and FS. Furthermore, we demonstrate the phase
control between these competing phases by the application of the external
magnetic field and external quasihydrostatic pressure.
