Abstract
An urban public transportation super-network model is established in this article. Compared with three existing complicated urban public transportation network models (the C-space network, L-space network, and P-space network), our urban public transportation super-network model first incorporated both station networks and bus line networks explicitly, which connects two non-homogeneous nodes (station and line nodes) through the notion of super networks. The proposed model reflects the interaction and mutual influences between the internal features and internal structures of the urban public transportation super network. And then the function projective synchronization of the dynamic public transportation super-network model is proven, and the high stability of the public transportation super network is confirmed by the Lyapunov stability theorem. Finally, the classical Lorenz chaotic system is applied in a numerical example to illustrate the proposed model and algorithm. The impact of departure frequency...
Highlights
The most complicated systems can be described by networks; a complicated network is typically used to describe complicated systems
The results provide theoretical foundations for optimizing public transportation networks and bus dispatching
This article explores the effects of departure frequency, line crowdedness, passenger transport density, and station dwell time on super network stability
Summary
The most complicated systems can be described by networks; a complicated network is typically used to describe complicated systems. One method to describe an urban public transportation network that adopts a complicated network uses bus lines as nodes. If two bus lines involve a common station, these two nodes are connected This method reflects the relationship of transferring between two bus lines. The method proposed in this article utilizes both stations and lines in the urban public transportation network as nodes. If two lines hold a common station, they are connected In this regard, a line-to-line network called an ‘‘L–L sub-network’’ can be established as follows. Mapping from an L–L sub-network to an S–S sub-network: This relationship reflects the stations on one bus line. We call such super network as a ‘‘line–station super network (L(S)SN).’’. The set of stations in S, which are related with li, is obtained as follows
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