Complete aggregation of the Lohe tensor model with the same free flow
Mathematical Physics
2020-10-28 v1 math.MP
Abstract
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.
Cite
@article{arxiv.2004.05406,
title = {Complete aggregation of the Lohe tensor model with the same free flow},
author = {Seung-Yeal Ha and Hansol Park},
journal= {arXiv preprint arXiv:2004.05406},
year = {2020}
}