  The SU($3$) Polyakov linear-sigma model (PLSM) in mean-field approximation is
utilized in analyzing the chiral condensates $\sigma_u$, $\sigma_d$, $\sigma_s$
and the deconfinement order parameters $\phi$, $\bar{\phi}$, at finite isospin
asymmetry. The bulk thermodynamics including pressure density, interaction
measure, susceptibility, and second-order correlations with baryon, strange and
electric charge quantum numbers are studied in thermal and dense medium. The
PLSM results are confronted to the available lattice QCD calculations. The
excellent agreement obtained strengthens the reliability of fixing the PLSM
parameters and therefore supports further predictions even beyond the scope of
the lattice QCD numerical applicability. From the QCD phase structure at finite
isospin chemical potential ($\mu_I$), a novel expression for the explicit
symmetry breaking term $h_3$ is introduced, we find that the pseudo-critical
temperatures decrease with the increase in $\mu_I$. We conclude that the QCD
phase structure in ($T_\chi$-$\mu_I$) plane seems to extend the one in
($T_\chi$-$\mu_B$) plane.
