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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 groupscan be identified with the Bruhat order on symmetric group, when all theeigenvalues of Lax matrix are distinct, or with the Bruhat order onpermutations of a multiset, if there are multiple eigenvalues. We show, thatthe coincidence of the phase portrait of Toda system and the Hasse diagram ofBruhat order holds in the case of arbitrary simple Lie groups of rank $2$: tothis end we need only to check this property for the two remaining groups ofsecond rank, $Sp(4,\mathbb R)$ and the real form of $G_2$.

Phase portraits of the generalized full symmetric Toda systems on rank 2 groups