Synchronization of networked phase oscillators depends essentially on the correlation between the topological structure of the graph and the dynamical property of the elements. We propose the concept of ＇reduced freq...Synchronization of networked phase oscillators depends essentially on the correlation between the topological structure of the graph and the dynamical property of the elements. We propose the concept of ＇reduced frequency＇, a measure which can quantify natural frequencies of each pair of oscillators. Then we introduce an evolving network whose linking rules are controlled by its own dynamical property. The simulation results indicate that when the linking probability positively correlates with the reduced frequency, the network undergoes a first-order phase transition. Meanwhile, we discuss the circumstance under which an explosive synchronization can be ignited. The numerical results show that the peculiar butterfly shape correlation between frequencies and degrees of the nodes contributes to an explosive synchronization transition.展开更多
Public transportation network reorganisation can be a key measure in designing more efficient networks and increasing the number of passengers. To date, several authors have proposed models for the “transit route net...Public transportation network reorganisation can be a key measure in designing more efficient networks and increasing the number of passengers. To date, several authors have proposed models for the “transit route network design problem” (TRNDP), and many of them use a transit assignment model as one component. However, not all models have considered the “common lines problem,” which is an essential feature in transit network assignment and is based on the concept that the fastest way to get to a destination is to take the first vehicle arriving among an “attractive” set of lines. Thus, we sought to reveal the features of considering the common lines problem by comparing results with and without considering the problem in a transit assignment model. For comparison, a model similar to a previous one was used, formulated as a bi-level optimisation problem, the upper problem of which is described as a multi-objective problem. As a result, although the solutions with and without considering the common lines showed almost the same Pareto front, we confirmed that a more direct service is provided if the common lines problem is considered whereas a less direct service is provided if it is not. With a small network case study, we found that considering the common lines problem in the TRNDP is important as it allows operators to provide more direct services.展开更多
基金Supported by the Open Fund from Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing under Grant No 2015CSOBDP0101the National Natural Science Foundation of China under Grant No11162019
文摘Synchronization of networked phase oscillators depends essentially on the correlation between the topological structure of the graph and the dynamical property of the elements. We propose the concept of ＇reduced frequency＇, a measure which can quantify natural frequencies of each pair of oscillators. Then we introduce an evolving network whose linking rules are controlled by its own dynamical property. The simulation results indicate that when the linking probability positively correlates with the reduced frequency, the network undergoes a first-order phase transition. Meanwhile, we discuss the circumstance under which an explosive synchronization can be ignited. The numerical results show that the peculiar butterfly shape correlation between frequencies and degrees of the nodes contributes to an explosive synchronization transition.
文摘Public transportation network reorganisation can be a key measure in designing more efficient networks and increasing the number of passengers. To date, several authors have proposed models for the “transit route network design problem” (TRNDP), and many of them use a transit assignment model as one component. However, not all models have considered the “common lines problem,” which is an essential feature in transit network assignment and is based on the concept that the fastest way to get to a destination is to take the first vehicle arriving among an “attractive” set of lines. Thus, we sought to reveal the features of considering the common lines problem by comparing results with and without considering the problem in a transit assignment model. For comparison, a model similar to a previous one was used, formulated as a bi-level optimisation problem, the upper problem of which is described as a multi-objective problem. As a result, although the solutions with and without considering the common lines showed almost the same Pareto front, we confirmed that a more direct service is provided if the common lines problem is considered whereas a less direct service is provided if it is not. With a small network case study, we found that considering the common lines problem in the TRNDP is important as it allows operators to provide more direct services.
