  The conventional Kibble-Zurek scaling describes the scaling behavior in the
driven dynamics across a single critical region. In this paper, we study the
driven dynamics across an overlapping critical region, in which a critical
region (Region-A) is overlaid by another critical region (Region-B). We develop
a hybridized Kibble-Zurek scaling (HKZS) to characterize the scaling behavior
in the driven process. According to the HKZS, the driven dynamics in the
overlapping region can be described by the critical theories for both Region-A
and Region-B simultaneously. This results in a constraint on the scaling
function in the overlapping critical region. We take the quantum Ising chain in
an imaginary longitudinal-field as an example. In this model, the critical
region of the Yang-Lee edge singularity and the critical region of the
ferromagnetic-paramagnetic phase transition point overlap with each other. We
numerically confirm the HKZS by simulating the driven dynamics in this
overlapping region. The HKZSs in other models are also discussed.
