论文标题
具有高阶多项式耦合的LOHE矩阵模型的梯度流式公式
A gradient flow formulation of the Lohe matrix model with a high-order polynomial coupling
论文作者
论文摘要
我们为通过梯度流量接近具有高阶耦合的同质集合提供了广义LOHE矩阵模型。对于具有相同哈密顿量的同质自由流，众所周知，具有立方联系的LOHE矩阵模型可以将其重新铸造为具有平方的平均frobenius norm的梯度系统。在本文中，我们进一步得出了通过梯度流量进近具有高阶耦合的广义LOHE矩阵模型，以获得多项式电位。对于提出的模型，我们还提供了一个足够的框架，以耦合强度和初始数据，从而导致同质集合的新兴动态。
We present a generalized Lohe matrix model for a homogeneous ensemble with higher order couplings via the gradient flow approach. For the homogeneous free flow with the same hamiltonian, it is well known that the Lohe matrix model with cubic couplings can recast as a gradient system with a potential which is a squared Frobenius norm of of averaged state. In this paper, we further derive a generalized Lohe matrix model with higher-order couplings via gradient flow approach for a polynomial potential. For the proposed model, we also provide a sufficient framework in terms of coupling strengths and initial data, which leads to the emergent dynamics of the homogeneous ensemble.
