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We study emergent dynamics of the Lohe hermitian sphere(LHS) model which canbe derived from the Lohe tensor model \cite{H-P2} as a complex counterpart ofthe Lohe sphere(LS) model. The Lohe hermitian sphere model describes aggregatedynamics 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 twocoupling terms. For identical ensemble with the same free flow dynamics, weprovide a sufficient framework leading to the complete aggregation in which allpoint particles form a giant one-point cluster asymptotically. In contrast, fornon-identical ensemble, we also provide a sufficient framework for thepractical aggregation. Our sufficient framework is formulated in terms ofcoupling strengths and initial data. We also provide several numerical examplesand compare them with our analytical results.

Emergent dynamics of the Lohe Hermitian sphere model with frustration