Synchronisation between two different networks with multi-weights and its application in public traffic network

The paper established a conventional bus traffic network and a subway network by using the method of space R based on the existing public traffic network model. Regarding these two networks as the sub-networks, this paper presented a new two-layer-coupled public traffic network with multi-weights through the transfer relationship between conventional bus lines and subway lines. Every edge of this model’s two sub-networks has one or several different property weights, and the coupling edges between two sub-networks have one weight. Based on the method of network split, the paper splits the complex networks with multi-weights into several different single-weighted two-layer-coupled public traffic networks and then investigates its global synchronisation. Finally, according to the synchronisation theory of coupling networks with multi-weights and taking ‘Lorenz system’ as the network node, some numerical examples are given to show the impact of congestion degree, passenger-flow density, transfer degree and capacity matching degree to the two-layer-coupled public traffic network balance.