  Complete magnetoelectric (ME) phase diagrams of orthorhombic $R$MnO$_{3}$
with and without magnetic moments on the $R$ ions have been established. Three
kinds of multiferroic ground states, the $ab$-cycloidal, the $bc$-cycloidal,
and the collinear $E$-type phases, have been identified by the distinct ME
responses. The electric polarization of the $E$-type phase dominated by the
symmetric spin exchange ($bm{S}_{i} cdot bm{S}_{j}$) is more than 10 times as
large as that of the $bc$-cycloidal phase dominated by the antisymmetric one
($bm{S}_{i} times bm{S}_{j}$), and the ME response is enhanced near the
bicritical phase boundary between these multiferroic phases of different
origins. These findings will provide an important clue for the development of
the magnetically induced multiferroics.
