| ABSTRACT |
We study emergent dynamics of the Lohe Hermitian sphere (LHS) model, which can be derived from the Lohe tensor model [S.-Y. Ha and H. Park, SIAM J. Appl. Dyn. Syst. 13, 1312-1342 (2020)] as a complex counterpart of the Lohe sphere model. The LHS model describes aggregate dynamics of point particles on the Hermitian sphere HSd lying in Cd+1, and the coupling terms in the LHS model consist of two terms. For an 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 a 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 analytical results. Published under license by AIP Publishing. |
