  We study emergent dynamics of the Lohe hermitian sphere (LHS) model with the
same free flows under the dynamic interplay between state evolution and
adaptive couplings. The LHS model is a complex counterpart of the Lohe sphere
(LS) model on the unit sphere in Euclidean space, and when particles lie in the
Euclidean unit sphere embedded in $\bbc^{d+1}$, it reduces to the Lohe sphere
model. In the absence of interactions between states and coupling gains,
emergent dynamics have been addressed in [22]. In this paper, we further extend
earlier results in the aforementioned work to the setting in which the state
and coupling gains are dynamically interrelated via two types of coupling laws,
namely anti-Hebbian and Hebbian coupling laws. In each case, we present two
sufficient frameworks leading to complete aggregation depending on the coupling
laws, when the corresponding free flow is the same for all particles.
