  Competition between ordered phases, and their associated phase transitions,
are significant in the study of strongly correlated systems. Here we examine
one aspect, the nonequilibrium dynamics of a photoexcited Mott-Peierls system,
using an effective Peierls-Hubbard model and exact diagonalization. Near a
transition where spin and charge become strongly intertwined, we observe
anti-phase dynamics and a coupling-strength-dependent suppression or
enhancement in the static structure factors. The renormalized bosonic
excitations coupled to a particular photoexcited electron can be extracted,
which provides an approach for characterizing the underlying bosonic modes. The
results from this analysis for different electronic momenta show an uneven
softening due to a stronger coupling near $k_F$. This behavior reflects the
strong link between the fermionic momenta, the coupling vertices, and
ultimately the bosonic susceptibilities when multiple phases compete for the
ground state of the system.
