论文标题
沮丧
Emergent dynamics of the Lohe Hermitian sphere model with frustration
论文作者
论文摘要
我们研究了Lohe Hermitian Sphere（LHS）模型的新兴动力学，该动力学可以从Lohe Tensor模型\ Cite {H-P2}作为Lohe Sphere（LS）模型的复杂对应物中得出。 Lohe Hermitian Sphere模型描述了Hermitian Sphere上的点粒子的总动力学$ \ BBH \ BBS^D $，位于$ {\ Mathbb C}^{d+1} $中，以及LHS模型中的耦合项由两个交换项组成。对于相同的自由流动动力学的相同集合，我们提供了一个足够的框架，导致完整的聚合，其中所有点粒子逐渐形成一个巨大的单点群集。相比之下，对于非相同的合奏，我们还为实际聚合提供了足够的框架。我们足够的框架是根据耦合强度和初始数据来制定的。我们还提供了几个数值示例，并将它们与我们的分析结果进行比较。
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.
