| مستخلص: |
We study emergent behaviors of the Lohe hermitian sphere (LHS) model which is an aggregation model on Cd. The LHS model is a complex analogue of the Lohe sphere model on Rd, and hermitian spheres are invariant sets for the LHS dynamics. For the derivation of the LHS model, we use a top-down approach, namely a reduction from a high-rank aggregation model, the Lohe tensor model. The Lohe tensor model is a first-order aggregation model on the space of tensors with the same rank and sizes, and it was first proposed by the authors in a recent work [J. Stat. Phys., 178 (2020), pp. 1268{1292]. In this work, we study how the LHS model appears as a special case of the Lohe tensor model, and for the proposed model, we provide a cross-ratio-like conserved quantity, a sufficient framework for the complete aggregation, and a uniform p-stability estimate with respect to initial data. [ABSTRACT FROM AUTHOR] |
