Equilibrium Problem for the Stochastic Multi-Weighted Urban Public Transportation System with Time Delay: A Graph-Theoretic Method

This paper focuses on the equilibrium problem of an urban public transportation system with time delay. Time delay, multi-weights, and stochastic disturbances are considered in the urban public transportation system. Hence, one can regard the urban public transportation system as a stochastic multi-weighted delayed complex network. By combining graph theory and the Lyapunov method, the global Lyapunov function is constructed indirectly. Moreover, the response system can realize synchronization with the drive system under the adaptive controller. In other words, the urban public transportation system is balanced in the actual running traffic network. Finally, numerical examples about the Chua system and small-world network are presented to confirm the accuracy and validity of the theoretical results.