## 4 Discussion and Conclusions  
Few studies have analyzed the competing relationships among conventional bus, rail, and cab subsystems from the perspective of urban public transportation systems, while fewer or insufficiently in-depth studies have been conducted on the advantageous spacing of various public travel modes in cities in cold regions. Existing studies are as follows: [PERSON] et al. [13] (2020) used the competition and cooperation index to define the competitiveness of bus and metro lines from a geospatial perspective based on the geographic location and service scope of metro and bus stations, but they lacked the consideration of passenger demand and service capacity of bus lines. [PERSON] et al. [20] (2022) analyzed the competitive relationship between cabs and the metro mainly considering the spatial heterogeneity of the built environment, characterizing it as competing with, extending, and complementing the metro, but they lacked a study of the intrinsic dynamics of competition. [PERSON] et al. [23] (2019) applied a two-layer planning model to describe the competition problem among private cars, cabs, buses, and rail transit in terms of mode choice and constructed a computational model for the rail transit sharing rate in cities in cold regions, but they did not further investigate the competition characteristics among multi-modal transit in cities in cold regions. Based on this, this paper considers the level of economic development of the cities in the cold area, the climate characteristics of the cities in the cold area during the ice and snow period, and the travel characteristics of the residents. We construct the model of multi-modal public transportation Lotka-Volterra competing relationship in the cities in the cold area, calibrate the model coefficients with the average competition coefficients and the role coefficients of the cities in the cold area, and combine them with the actual passenger volume and growth rate of the various modes of transportation in the cold area city. We simulate and analyze the multi-modal public transportation competing relationship in the cities in the cold area, as well as the mechanism of the evolution of the competing between the conventional buses and the rail transportation. The major contributions of this study are summarized as follows. 1. The Lotka-Volterra model is transformed with transportation significance, so that the parameters in the model have more significance in the field of transportation, which is suitable for analyzing the complex competitive relationship between multiple modes of transportation;
2. Considering that conventional buses and rail transit are mainly dominant in urban transit systems in cold regions, the competition influence effect coefficients and cooperation influence effect coefficients are introduced to analyze the mechanism of the evolution of the competition between conventional buses and rail transit in cities in cold regions;
3. Rail transit has the advantages of rapidity, punctuality, and comfort in urban medium- and long-distance transportation, and cabs are more flexible and convenient in urban medium- and short-distance transportation, with better accessibility, which is suitable for individual rides or specific needs, and therefore, rail transit and cab travel modes have an inhibiting effect on the development of conventional transportation;* The system dynamics of the direction of the evolution of the competitive relationship between rail transit and surface buses lies in the strength of competition or cooperation between the two sides;
* In the competition environment, due to the existence of a certain degree of cooperation with each other, even if the competition is too intense, the disadvantaged party extinction time will be greatly delayed.