论文标题
在Schrödinger-Lohe层次结构上，用于聚集及其新兴动态
On the Schrödinger-Lohe hierarchy for aggregation and its emergent dynamics
论文作者
论文摘要
LOHE层次结构是由Kuramoto模型，复杂LOHE球模型，Lohe矩阵模型和LOHE Tensor模型组成的有限维聚合模型的层次结构。相反，Schrödinger-Lohe模型是文献中唯一已知的无限二维LOHE聚合模型。在本文中，我们提供了Schrödinger-Lohe模型与复杂的LOHE球体模型之间的明确联系，然后通过利用这种显式关系，我们构建了Lohe矩阵的无限维升降机和Lohe Tensor模型。通过这种方式，我们建立了与Lohe层次结构的无限维度扩展相对应的Schrödinger-Lohe层次结构。对于拟议的层次结构，我们提供了足够的框架，从而从耦合强度和初始配置方面提供了完整的聚合。
The Lohe hierarchy is a hierarchy of finite-dimensional aggregation models consisting of the Kuramoto model, the complex Lohe sphere model, the Lohe matrix model and the Lohe tensor model. In contrast, the Schrödinger-Lohe model is the only known infinite-dimensional Lohe aggregation model in literature. In this paper, we provide an explicit connection between the Schrödinger-Lohe model and the complex Lohe sphere model, and then by exploiting this explicit relation, we construct infinite-dimensional liftings of the Lohe matrix and the Lohe tensor models. In this way, we establish the Schrödinger-Lohe hierarchy which corresponds to the infinite-dimensional extensions of the Lohe hierarchy. For the proposed hierarchy, we provide sufficient frameworks leading to the complete aggregation in terms of coupling strengths and initial configurations.
