论文标题
Lohe Hermitian Sphere模型的集体行为与惯性
Collective behaviors of the Lohe hermitian sphere model with inertia
论文作者
论文摘要
我们提出了一阶Lohe Hermitian Sphere（LHS）模型的二阶扩展，并研究其新兴的渐近动力学。我们提出的模型将惯性效应作为二阶扩展。惯性项可以在较小的时间间隔（初始层）中产生粒子轨迹的振荡行为，这在应用基于单调性的参数的应用方面造成了技术困难。对于紧急估计，我们采用两点相关函数，该函数被定义为粒子位置之间的内部产物。对于具有相同频率矩阵的同质集合，我们在系统参数和初始数据方面提供了两个足够的框架，以表明两个点相关函数趋向于与完整的聚合完全相同的统一。相反，对于具有不同频率矩阵的异质集合，我们就系统参数和初始数据提供了足够的框架，这使两点相关功能通过提高主耦合强度接近统一。
We present a second-order extension of the first-order Lohe hermitian sphere(LHS) model and study its emergent asymptotic dynamics. Our proposed model incorporates an inertial effect as a second-order extension. The inertia term can generate an oscillatory behavior of particle trajectory in a small time interval(initial layer) which causes a technical difficulty for the application of monotonicity-based arguments. For emergent estimates, we employ two-point correlation function which is defined as an inner product between positions of particles. For a homogeneous ensemble with the same frequency matrix, we provide two sufficient frameworks in terms of system parameters and initial data to show that two-point correlation functions tend to the unity which is exactly the same as the complete aggregation. In contrast, for a heterogeneous ensemble with distinct frequency matrices, we provide a sufficient framework in terms of system parameters and initial data, which makes two-point correlation functions close to unity by increasing the principal coupling strength.
