  We study quantitative homogenization of the eigenvalues for elliptic systems
with periodically distributed inclusions, where the conductivity of inclusions
are strongly contrast to that of the matrix. We propose a quantitative version
of periodic unfolding method, based on this and the recent results concerned on
high-contrast homogenization, the convergence rates of eigenvalues are studied
for any contrast $\delta \in (0,\infty)$.
