Analysis of the projective synchronization of the urban public transportation super network

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, line crowdedness, passenger transport density, and station dwell time on synchronous ability of the urban public transportation super-network model is analyzed. So, this study is a discussion on the urban public transportation super-network balance in order to offer theoretical basis for people to research bus dispatching and bus lines optimization.