论文标题
与相同自由流的LOHE张量模型的完全聚合
Complete aggregation of the Lohe tensor model with the same free flow
论文作者
论文摘要
LOHE张量模型是一种张张值的一阶张量值连续时间模型，用于张紧量级和大小相同的张量。它减少了众所周知的聚合模型，例如kuramoto模型，LOHE球模型和LOHE矩阵模型，作为低级数张量的特殊情况。我们提出了一个足够的溶液分裂特性（SSP）的框架，并分析两个可能从一组初始数据中出现的可能的渐近状态（完全骨料状态和双极状态）。此外，我们提供了一个足够的框架，从而在初始数据和系统参数方面为上述两个渐近状态提供了框架。
The Lohe tensor model is a first-order tensor-valued continuous-time model for the aggregation of tensors with the same rank and size. It reduces to well-known aggregation models such as the Kuramoto model, the Lohe sphere model and the Lohe matrix model as special cases for low-rank tensors. We present a sufficient and necessary framework for the solution splitting property(SSP) and analyze two possible asymptotic states(completely aggregate state and bi-polar state) which can emerge from a set of initial data. Moreover, we provide a sufficient framework leading to the aforementioned two asymptotic states in terms of initial data and system parameters.
