The honk effect is not uncommon in the real traffic and may exert great influence on the stability of traffic flow. As opposed to the linear description of the traditional one-dimensional lattice hydrodynamic model, the high-dimensional lattice hydrodynamic model is a gridded analysis of the real traffic environment, which is a generalized form of the one-dimensional lattice model. Meanwhile, the high-dimensional traffic flow exposed to the open-ended environment is more likely to be affected by the honk effect. In this paper, we propose an extension of two-dimensional triangular lattice hydrodynamic model under honk environment. The stability condition is obtained via the linear stability analysis, which shows that the stability region in the phase diagram can be effectively enlarged under the honk effect. Modified Korteweg–de Vries equations are derived through the nonlinear stability analysis method. The kink–antikink solitary wave solution is obtained by solving the equation, which can be used to describe the propagation characteristics of density waves near the critical point. Finally, the simulation example verifies the correctness of the above theoretical analysis.

中文翻译：

---

喇叭环境下的一种修正二维三角点阵模型

喇叭效应在实际交通中并不少见，可能对交通流的稳定性产生很大影响。与传统一维格子水动力模型的线性描述相反，高维格子水动力模型是对真实交通环境的网格化分析，是一维格子模型的推广形式。同时，暴露在开放式环境中的高维交通流更容易受到喇叭效应的影响。在本文中，我们提出了在喇叭环境下二维三角晶格流体动力学模型的扩展。通过线性稳定性分析得到稳定条件，表明在喇叭效应下，相图中的稳定区域可以有效扩大。通过非线性稳定性分析方法推导出修正的 Korteweg-de Vries 方程。通过求解方程得到扭结-反扭结孤波解，可以用来描述密度波在临界点附近的传播特性。最后通过仿真算例验证了上述理论分析的正确性。