论文标题
从Lohe Tensor模型到Lohe Hermitian Sphere模型和新兴动态
From the Lohe tensor model to the Lohe Hermitian sphere model and emergent dynamics
论文作者
论文摘要
我们研究了Lohe Hermitian Sphere（LHS）模型的新兴行为，该模型是$ {\ Mathbb C}^D $的聚合模型。 LHS模型是$ {\ Mathbb r}^d $上Lohe Sphere模型的复杂类似物，Hermitian球体是LHS Dynamics的不变集。对于LHS模型的推导，我们使用自上而下的方法，即从高级聚合模型中减少了“ $ \ textIt {the lohe tensor模型} $。 LOHE张量模型是在具有相同等级和尺寸的张量的张量的一阶聚合模型，作者最初是在最近的工作中提出的。在这项工作中，我们研究了LHS模型如何作为LOHE张量模型的特殊情况，对于拟议的模型，我们提供了诸如保守数量的交叉比例，完全聚集的足够框架以及相对于初始数据的均匀$ \ ell^p $稳定性估计。
We study emergent behaviors of the Lohe hermitian sphere(LHS) model which is an aggregation model on ${\mathbb C}^d$. The LHS model is a complex analog of the Lohe sphere model on ${\mathbb R}^d$, 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, "$\textit{the Lohe tensor model}$." 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 \cite{H-P}. 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 $\ell^p$-stability estimate with respect to initial data.
