  We study emergent dynamics of the Lohe hermitian sphere(LHS) model which can
be derived from the Lohe tensor model \cite{H-P2} as a complex counterpart of
the Lohe sphere(LS) model. The Lohe hermitian sphere model describes aggregate
dynamics of point particles on the hermitian sphere $\bbh\bbs^d$ lying in
${\mathbb C}^{d+1}$, and the coupling terms in the LHS model consist of two
coupling terms. For identical ensemble with the same free flow dynamics, we
provide a sufficient framework leading to the complete aggregation in which all
point particles form a giant one-point cluster asymptotically. In contrast, for
non-identical ensemble, we also provide a sufficient framework for the
practical aggregation. Our sufficient framework is formulated in terms of
coupling strengths and initial data. We also provide several numerical examples
and compare them with our analytical results.
