  In this paper we continue investigations that we began in our previous works,
where we proved, that the phase diagram of Toda system on special linear groups
can be identified with the Bruhat order on symmetric group, when all the
eigenvalues of Lax matrix are distinct, or with the Bruhat order on
permutations of a multiset, if there are multiple eigenvalues. We show, that
the coincidence of the phase portrait of Toda system and the Hasse diagram of
Bruhat order holds in the case of arbitrary simple Lie groups of rank $2$: to
this end we need only to check this property for the two remaining groups of
second rank, $Sp(4,\mathbb R)$ and the real form of $G_2$.
