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.

中文翻译：

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具有相同自由流的 Lohe 张量模型的完全聚合

Lohe 张量模型是一阶张量值连续时间模型，用于聚合具有相同秩和大小的张量。它简化为众所周知的聚合模型，例如 Kuramoto 模型、Lohe 球模型和 Lohe 矩阵模型，作为低秩张量的特殊情况。我们为解分裂特性（SSP）提出了一个充分且必要的框架，并分析了可以从一组初始数据中出现的两种可能的渐近状态（完全聚合状态和双极状态）。此外，我们提供了一个足够的框架，导致在初始数据和系统参数方面的上述两种渐近状态。