Research on evolution dynamics of urban rail transit network based on allometric growth relationship

Each stage of the construction of the rail transit network has unique dynamic characteristics. It can provide recommendations for rail transit network planning and phased construction by evaluating the degree of evolution of the urban rail transit network and dividing the evolution stages precisely. Starting from the allometric growth relationship between transfer nodes and ordinary nodes in the urban rail transit network, this paper defines the evolution level of the rail transit network and the growth rate difference between transfer nodes and ordinary nodes and deduces the dynamic logistic equation of URT network evolution level using the mathematical derivative and logarithmic relationship. This paper reveals the dynamic law of the evolution process of the urban rail transit network at a theoretical level, analyzes the dynamic evolution process on this basis, determines the threshold for phasing the evolution stage, and divides it into four evolution stages. Finally, the results of the theoretical derivation are validated by the evolution data of the Beijing Rail Transit Network (1984–2020) over 45 years. The verification results are substantially congruent with the conclusions of the theoretical derivation, demonstrating the accuracy of the theoretical model and its practical usefulness in directing the building of the rail transit network.