论文标题
广义LOHE矩阵模型的新兴行为
Emergent Behaviors of the generalized Lohe matrix model
论文作者
论文摘要
我们在复杂矩阵的空间上提出了一个一阶聚合模型，该模型可以从LOHE Tensor模型衍生在具有相同等级和大小的张量的张量。我们将这种矩阵值的聚合模型称为“广义LOHE矩阵模型”。对于具有两个立方耦合术语的拟议矩阵模型，我们研究了几种结构特性，例如保护定律，解决方案分裂特性。特别是，对于仅一个耦合的情况，我们将减少的LOHE矩阵模型重新制定到具有对角挫败感的Lohe矩阵模型中，并提供了几个足够的框架，从而导致完整而实用的聚集。对于集体动力学的估计值，我们使用衡量聚合程度的集合直径使用非线性功能方法。
We present a first-order aggregation model on the space of complex matrices which can be derived from the Lohe tensor model on the space of tensors with the same rank and size. We call such matrix-valued aggregation model as "the generalized Lohe matrix model". For the proposed matrix model with two cubic coupling terms, we study several structural properties such as the conservation laws, solution splitting property. In particular, for the case of only one coupling, we reformulate the reduced Lohe matrix model into the Lohe matrix model with a diagonal frustration, and provide several sufficient frameworks leading to the complete and practical aggregations. For the estimates of collective dynamics, we use a nonlinear functional approach using an ensemble diameter which measures the degree of aggregation.
