Abstract: In view of the competition-cooperation relationship between rail transit and conventional bus and its development and evolution, combined with the ecological characteristics of the development of the two transportation modes, an adaptive inter-modal competition evolution model was established based on the Lotka-Volterra model of interspecific competition. Through the stability analysis of the equilibrium state of the proposed model, the internal dynamic mechanism of the evolution of the two traffic modes and the evolution path of different equilibrium states were discussed. Taking Shanghai, Nanjing and Xi’an as examples, the feasibility and applicability of the improved model were verified. The research results show that: compared with the standard Lotka-Volterra model, the improved model is closer to the evolution of actual competition between rail transit and conventional bus. The relative errors of the simulation data of Shanghai, Nanjing and Xi’an are reduced by 2.96%, 17.51% and 29.39% respectively. In different traffic environments, the two modes of transportation have different co-opetition effects, causing factors such as competition coefficients to fluctuate, which in turn affects the evolution of the competitive evolution between the two modes of transportation, and makes equilibrium state mutate and transit to a new, more coordinated and orderly state of equilibrium.

Key words: traffic and transportation engineering, rail transit, conventional bus, competition-cooperation relationship, Lotka-Volterra model, grey estimation method

摘要： 针对轨道交通与常规公交之间的竞合关系及其发展演变问题，结合2种交通方式发展过程中的生态学特征，以种间竞争Lotka-Volterra模型为基础，建立了具有自适应性的交通方式间竞争演变模型。通过对该模型平衡态的稳定性分析，探讨了2种交通方式演化的内在动力机制以及不同平衡态的演化路径。并以上海、南京和西安为例，验证改进模型的可行性和适用性。研究结果表明：与标准Lotka-Volterra模型相比，改进的模型更接近于轨道交通与常规公交的实际竞争演化，上海、南京和西安3个城市模拟数据的相对误差分别降低了2.96%、17.51%和29.39%；不同交通环境下，2种交通方式间具有不同的竞合效应，造成竞争系数等因素涨落，进而波及到2种交通方式的竞争演变，使得平衡态发生突变，跃迁到更为协调有序的新平衡态。

关键词: 交通运输工程, 轨道交通；常规公交；竞合关系；Lotka-Volterra模型；灰色估计法