复杂网络同步理论在城市公交网络中的应用研究
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摘要
随着城市规模不断扩大,机动车保有量急剧增加,城市交通拥堵问题日益严重。通过修建更多的道路可以提高路网的容量,缓解拥堵,但由于城市中可供修建道路的空间有限,而且道路建设的步伐远远跟不上交通需求增长的速度,交通拥堵现象仍然十分严重。国内外许多城市发展的经验表明,优先发展公共交通是解决城市交通拥堵问题的有效途径之一。
优化公交调度方案是优先发展公交的具体措施之一。本文运用复杂网络理论构造了三种公交网络模型,通过BA无标度网络理论分析城市公交网络的拓扑结构性质。进而分别考虑了带有时滞和时变时滞的复杂城市公交网络,运用复杂网络的同步理论对上述两种公交调度复杂网络模型进行了深入的研究。通过对兰州市城市公交网络和郑州市快速公交网络的实证研究和数值仿真验证了该模型的正确性和有效性。
本文主要从以下方面进行了研究：
(1)对复杂网络同步理论及公交调度理论的国内外研究现状进行了综述,深入研究了具有时滞复杂网络和时变时滞复杂网络的同步方法,运用延迟动力学系统的稳定性理论分析了依赖于时滞和时变时滞两种情况下系统全局同步的准则。
(2)针对城市公交网络的不同特征构造了三种公交网络模型：公交停靠站点网络模型、公交换乘网络模型、公交线路网络模型,研究了这三种网络模型的动力学性质、拓扑结构性质以及可靠性,证明其具有BA无标度网络特性,为后文运用复杂网络同步理论分析公交调度问题奠定了基础。
(3)在城市实际公交车辆运营过程中,由于车辆个体之间运行速度存在差异、交叉路口的控制信号器、突发事件等因素的影响,必然存在时延现象。本文建立了时滞公交线路网络模型,并给出了该模型的同步判据,进而利用节点含有时滞的复杂网络同步理论对城市公交系统进行“静态”调度研究,分析了乘客流量的演化过程。通过兰州市城市公交网络的实例分析和数值仿真验证了该方法能有效的优化常规公交调度方案。
(4)在城市公交网络实际运行过程中,由于不同时段路况、车流量、客流量等因素的影响,必然导致时变时滞现象发生,针对上述现象构造了节点含有时变时滞的公交线路网络模型,并研究了其动力学性质,利用节点含有时变时滞的复杂网络同步理论对城市公交网络进行“动态”调度研究。根据客流量的演变过程,选取非线性系统,通过理论分析和数值仿真实现了城市公交网络的协调调度,使运营车辆和出行乘客达到动态平衡,提高了运营效率。
(5)近年来,快速公交在一些人口较密集的发达城市得到了快速发展,提高城市快速公交的运行效率显得尤为重要。本文根据快速公交运行特征,构造了时变时滞快速公交网络模型,研究了快速公交网络的动力学性质及拓扑结构性质,证明其同样满足BA无标度网络特性。运用含有时变时滞的复杂网络同步理论对郑州市快速公交网络进行实例分析,模拟节点的客流量变化率,得出合理的调度方案,使快速公交线路在运营过程实现动态平衡,提高了运营效率,节省了运营成本。
With the scale of city unceasingly expanding, the number of vehicles rapidly increases, and the problem of urban traffic congestion has become increasingly serious. The traffic jam can be reduced through constructing more roads, which is used to enhance the capacity of road network. However, the speed of construction of road is far behind the growth rate of traffic demand, as the limited space of cities, which is available for the construction of roads, and the phenomenon of traffic congestion is still very serious. The experience of many cities in domestic and overseas shows that giving priority to the development of public transportation is one of effective way to solve urban traffic congestion.
The optimization of bus scheduling scheme is one of the specific measures for giving priority to the development of public transport. In this paper, three kinds of public transportation network models are built based on complex networks theory. And the topology properties of public transportation are analyzed through BA scale-free network theory. Moreover, the complex urban public transport networks with time delays and time-varying delays are considered respectively. Then, the two types of bus dispatch models of complex networks are deeply analyzed using synchronization theory of complex networks. The correctness and validity of these models are verified through experiment researches and numerical simulations of public transportation networks in Lanzhou and Bus Rapid Transit (BRT) network in Zhengzhou.
The main research works in this thesis are as follows:
(1) The research current situation of synchronization theory of complex networks and theory of bus dispatching at home and abroad is overviewed. The synchronization methods of complex networks with time-delay and time-varying delay are studied deeply. The criteria for global synchronization of systems with time-delay and time-varying delay are analyzed using the stability theory of time delay dynamic systems.
(2) Three different models:network model for bus stop, network model for bus ride and network model for bus line, are built based on different characteristics of public transit network of cities. The dynamical characteristics, topology properties and reliability of these three network models are studied. The BA scale-free characters, which lay the foundation for solving the problem of bus dispatching using the theory of synchronization of complex networks, are found in all these three models.
(3) In the actual operation of urban public transportation vehicles, the time-delay phenomenon is inherent, as the different speed between vehicles, control sjgnal detector in intersection, emergency and so on. In this thesis, the models of public transportation networks with time-delay are built and the criteria of synchronization of these models are given. Then the "static" scheduling of public transport system is stuied and the evolution process of passenger flow is analyzed based on the synchronization theory of complex networks'nodes with time-delay. The effectness of this method to optimize conventional bus dispatching scheme is proved through numerical simulations and example analysis of public transportation network of Lanzhou.
(4) In the actual operation of urban public transportation networks, the time-varying delaying phenomenon is inherent, because of road conditions, traffic volumes, passenger volumes and other factors and so on at different times. The models of public transportation networks'nodes with time-varying delay are built against the above phenomena, and the dynamic properties of these models are studied. Then the "dynamic" scheduling of urban transit system, which can be used to improve operation efficiency and helps the running vehicles and passengers reach dynamical equilibrium, is realized through theoretical analysis and numerical simulation by choosing appropriate nonlinear systems according to the evolution process of passenger volumes.
(5) In recent years, BRT in some densely populated prosperous cities have developed rapidly. It is particularly important to improve the operating efficiency of BRT. In this thesis, the BRT models with time-varying delay are built, and the dynamical properties and the topology properties of BRT networks are studied based on the operating characteristics of BRT. And the BA scale-free properties are found in these BRT models. The BRT networks of Zhengzhou are analyzed based on the theory of synchronization theory of complex networks with time-varying delay. The passenger volumes rates of change at the nodes are caculated and the optimalizing scheduling schemes are gained. All of these operations can help the running BRT reach dynamical equilibrium, improve operation efficiency and save operation costs.
优化公交调度方案是优先发展公交的具体措施之一。本文运用复杂网络理论构造了三种公交网络模型,通过BA无标度网络理论分析城市公交网络的拓扑结构性质。进而分别考虑了带有时滞和时变时滞的复杂城市公交网络,运用复杂网络的同步理论对上述两种公交调度复杂网络模型进行了深入的研究。通过对兰州市城市公交网络和郑州市快速公交网络的实证研究和数值仿真验证了该模型的正确性和有效性。
本文主要从以下方面进行了研究：
(1)对复杂网络同步理论及公交调度理论的国内外研究现状进行了综述,深入研究了具有时滞复杂网络和时变时滞复杂网络的同步方法,运用延迟动力学系统的稳定性理论分析了依赖于时滞和时变时滞两种情况下系统全局同步的准则。
(2)针对城市公交网络的不同特征构造了三种公交网络模型：公交停靠站点网络模型、公交换乘网络模型、公交线路网络模型,研究了这三种网络模型的动力学性质、拓扑结构性质以及可靠性,证明其具有BA无标度网络特性,为后文运用复杂网络同步理论分析公交调度问题奠定了基础。
(3)在城市实际公交车辆运营过程中,由于车辆个体之间运行速度存在差异、交叉路口的控制信号器、突发事件等因素的影响,必然存在时延现象。本文建立了时滞公交线路网络模型,并给出了该模型的同步判据,进而利用节点含有时滞的复杂网络同步理论对城市公交系统进行“静态”调度研究,分析了乘客流量的演化过程。通过兰州市城市公交网络的实例分析和数值仿真验证了该方法能有效的优化常规公交调度方案。
(4)在城市公交网络实际运行过程中,由于不同时段路况、车流量、客流量等因素的影响,必然导致时变时滞现象发生,针对上述现象构造了节点含有时变时滞的公交线路网络模型,并研究了其动力学性质,利用节点含有时变时滞的复杂网络同步理论对城市公交网络进行“动态”调度研究。根据客流量的演变过程,选取非线性系统,通过理论分析和数值仿真实现了城市公交网络的协调调度,使运营车辆和出行乘客达到动态平衡,提高了运营效率。
(5)近年来,快速公交在一些人口较密集的发达城市得到了快速发展,提高城市快速公交的运行效率显得尤为重要。本文根据快速公交运行特征,构造了时变时滞快速公交网络模型,研究了快速公交网络的动力学性质及拓扑结构性质,证明其同样满足BA无标度网络特性。运用含有时变时滞的复杂网络同步理论对郑州市快速公交网络进行实例分析,模拟节点的客流量变化率,得出合理的调度方案,使快速公交线路在运营过程实现动态平衡,提高了运营效率,节省了运营成本。
With the scale of city unceasingly expanding, the number of vehicles rapidly increases, and the problem of urban traffic congestion has become increasingly serious. The traffic jam can be reduced through constructing more roads, which is used to enhance the capacity of road network. However, the speed of construction of road is far behind the growth rate of traffic demand, as the limited space of cities, which is available for the construction of roads, and the phenomenon of traffic congestion is still very serious. The experience of many cities in domestic and overseas shows that giving priority to the development of public transportation is one of effective way to solve urban traffic congestion.
The optimization of bus scheduling scheme is one of the specific measures for giving priority to the development of public transport. In this paper, three kinds of public transportation network models are built based on complex networks theory. And the topology properties of public transportation are analyzed through BA scale-free network theory. Moreover, the complex urban public transport networks with time delays and time-varying delays are considered respectively. Then, the two types of bus dispatch models of complex networks are deeply analyzed using synchronization theory of complex networks. The correctness and validity of these models are verified through experiment researches and numerical simulations of public transportation networks in Lanzhou and Bus Rapid Transit (BRT) network in Zhengzhou.
The main research works in this thesis are as follows:
(1) The research current situation of synchronization theory of complex networks and theory of bus dispatching at home and abroad is overviewed. The synchronization methods of complex networks with time-delay and time-varying delay are studied deeply. The criteria for global synchronization of systems with time-delay and time-varying delay are analyzed using the stability theory of time delay dynamic systems.
(2) Three different models:network model for bus stop, network model for bus ride and network model for bus line, are built based on different characteristics of public transit network of cities. The dynamical characteristics, topology properties and reliability of these three network models are studied. The BA scale-free characters, which lay the foundation for solving the problem of bus dispatching using the theory of synchronization of complex networks, are found in all these three models.
(3) In the actual operation of urban public transportation vehicles, the time-delay phenomenon is inherent, as the different speed between vehicles, control sjgnal detector in intersection, emergency and so on. In this thesis, the models of public transportation networks with time-delay are built and the criteria of synchronization of these models are given. Then the "static" scheduling of public transport system is stuied and the evolution process of passenger flow is analyzed based on the synchronization theory of complex networks'nodes with time-delay. The effectness of this method to optimize conventional bus dispatching scheme is proved through numerical simulations and example analysis of public transportation network of Lanzhou.
(4) In the actual operation of urban public transportation networks, the time-varying delaying phenomenon is inherent, because of road conditions, traffic volumes, passenger volumes and other factors and so on at different times. The models of public transportation networks'nodes with time-varying delay are built against the above phenomena, and the dynamic properties of these models are studied. Then the "dynamic" scheduling of urban transit system, which can be used to improve operation efficiency and helps the running vehicles and passengers reach dynamical equilibrium, is realized through theoretical analysis and numerical simulation by choosing appropriate nonlinear systems according to the evolution process of passenger volumes.
(5) In recent years, BRT in some densely populated prosperous cities have developed rapidly. It is particularly important to improve the operating efficiency of BRT. In this thesis, the BRT models with time-varying delay are built, and the dynamical properties and the topology properties of BRT networks are studied based on the operating characteristics of BRT. And the BA scale-free properties are found in these BRT models. The BRT networks of Zhengzhou are analyzed based on the theory of synchronization theory of complex networks with time-varying delay. The passenger volumes rates of change at the nodes are caculated and the optimalizing scheduling schemes are gained. All of these operations can help the running BRT reach dynamical equilibrium, improve operation efficiency and save operation costs.
引文
[1]徐吉万,徐冬玲.城市交通的计算机控制和管理[M].北京：测绘出版社,1988.
[2]王炜,杨新苗,陈学武.城市公共交通系统规划方法与管理技术[M].北京：科学出版社,2002.
[3]Strogatz S H. Exploring complex networks[J]. Nature,2001,410:268-276.
[4]Barabasi A L, Albert R. Emergence of scaling in random networks[J]. Science,1999,286:509-512.
[5]Barabasi A L, Albert R, Jeong H. Mean-field theory for scale-free random networks[J]. Physical A, 1999,272:173-187.
[6]Watts D J, Strogatz S H. Collective dynamical of'small-world' networks[J]. Nature,1998,393: 440-442.
[7]Jeong H, Tombor B, Albert R, Oltvai Z, Barabasi A L. The large-scale organization of metabolic networks[J]. Nature,2000,407:651-654.
[8]Jin C W, Marsden I, Chen X Q, Liao X B. Dynamic DNA contacts observed in the NMR structure of winged Helix Protein-DNA Complex[J].Molecular Biology,1999,289:683-690.
[9]Newman M E J. The structure and functions of complex networks[J]. SIAM Rev,2003,45:167-256.
[10]Lu J H, Yu X H, Chen G R. Chaos synchronization of general complex dynamical networks[J]. Physica A,2004,334:281-302.
[11]Wang X F, Chen G R. Synchronization in small-word dynamical networks[J]. Int. J. Bifur. Chaos 2002,12(1):187-192.
[12]Wang X F, Chen G R. Synchronization in scale-free dynamical networks:Robustness and fragilityfJ]. IEEE Trans. Circuits and Systems,2002,49 (1):54-62.
[13]Hong H, Choi M Y, Kim B J. Synchronization on small-world networks[J]. Phys. Rev. E, 2002,65(2):026139(5).
[14]Barahona M, Pecora L M. Synchronization in small-world systems[J]. Phys. Rev. Lett.,2002,89(5): 054101.
[15]Lu J H, Yu X H, Chen G R, Cheng D Z. Characterizing the synchronizability of small-world dynamical networks[J]. IEEE Trans.Circuits and Systems,2004,51(4):787-796.
[16]冯存芳.时滞混沌系统的同步及复杂网络上的动力学行为[D].博士学位论文,兰州：兰州大学,2009.
[17]赵明.复杂网络上动力系统同步现象[D].(博士学位论文).合肥：中国科学技术大学,2007.
[18]戴杨.耦合时滞复杂网络的同步性研究[D].(博士学位论文).上海：上海交通大学,2009.
[19]钱伟.时滞系统的若干问题的研究[D].(博士学位论文).杭州：浙江大学,2009.
[20]赵跃辉.带有时变时滞的复杂动态网络的同步准则[D].(硕士学位论文).武汉：武汉理工大学,2009.
[21]张好智.城市交通网络设计问题的相关优化模型与算法[D].(博士学位论文).北京：北京交通大学,2007.
[22]Lu W L, Chen T P. Synchronization of coupled connected neural networks with delays [J]. IEEE Transactions on Circuits and Systems I,2004,51(12):2491-2503.
[23]Lu J H, Chen G R. A new chaotic attractor coined. International Journal of Bifurcation and Chaos [J],2002,12(3):659-661.
[24]Wu J S, Jiao L C. Synchronization in complex delayed dynamical networks with nonsymmetric coupling [J]. Physica A,2007,386:513-530.
[25]Wu X. Synchronization based topology identification of weighted general complex dynamical networks with time-varying coupling delay [J]. Physica A,2008,387:997-1008.
[26]Yu W W, Cao J D. Adaptive Q-S (lag. anticipated, and complete) time-varying synchronization and parameters identification of uncertain delayed neural networks[J]. Chaos,2006,16:023119.
[27]Yu W W, Cao J D. Adaptive synchronization and lag synchronization of uncertain dynamical system with time delay based on parameter identification[J]. Physica A,2007,375(2):467-482.
[28]Zhou J, Xiang L, Liu Z R. Global synchronization in general complex delayed dynamical networks and its applications[J]. IEEE Transactions on Automatic Control,2007,385(2):729-742.
[29]Cai S M, Zhou J, Xiang L, Liu Z R. Robust impulsive synchronization of complex delayed dynamical networks[J]. Physics Letters A,2008,372(30):4990-4995.
[30]Li C G, Chen G R. Synchronization in general complex dynamical networks with coupling delays[J]. Physica A,2004,343:263-278.
[31]Gao H J, Lam J, Chen G R. New criteria for synchronization stability of general complex dynamical networks with coupling delays[J]. Physics Letters A,2006,360:263-273.
[32]Wu J S, Jiao L C. Synchronization in dynamic networks with nonsymmetrical time-delay coupling based on linear feedback controllers [J].Physica A:Statistical Mechanics and its Applications,2008,387 (8-9):2111-2119.
[33]Zhou J, Lu J A, Lii J H. Adaptive synchronization of an uncertain complex dynamical network[J]. Physica A,2006,51(4):652-656.
[34]Zhou J, Chen T P. Synchronization in general complex delayed dynamical networks[J]. IEEE Transactions on Circuits and Systems-I:Regular Papers,2006,53(3):733-744.
[35]Zhou J, Xiang L, Liu Z R. Synchronization in complex delayed dynamical networks with impulsive effects[J]. Physica A,2007,384(2):684-692.
[36]Wang Q Y, Duan Z S, Chen G R, Feng Z S. Synchronization in a class of weighted complex networks with coupling delays[J]. Physica A:Statistical Mechanics and its Applications,2008,387(22):5616-5622.
[37]Xiang L Y, Liu Z X, Chen Z Q. Pinning control of complex dynamical networks with general topology[J]. Physica A,2007,379(1):298-306.
[38]Li C P, Sun W G, Kurths J. Synchronization of complex dynamical networks with time delays [J]. Physia A,2006,361:24-34.
[39]Wang L, Dai H p, Dong H, et al. Adaptive synchronization of weighted complex dynamical networks with coupling time-varying delays [J]. Physics Letters A,2008,372:3632-3639.
[40]Zheng S, Bi Q H, Cai G L. Adaptive projective synchronization in complex networks with time-varying coupling delay [J]. Physics Letters A,2009,373:1553-1559.
[41]Koo J H, Ji D H, Won S C. Synchronization of singular complex dynamical networks with time-varying delays [J]. Applied Mathematics and Computation,2010,217(8):3916-3923.
[42]Tang Y, Fang J A, Xia M, et al. Synchronization of Takagi-Sugeno fuzzy stochastic discrete-time complex networks with mixed time varying delays [J].Applied Mathematical Modelling,2010,34:843-855.
[43]Zuo Z Q, Yang C L, Wang Y J. A unified framework of exponential synchronization for complex networks with time-varying delays [J]. Physics Letters A,2010,374:1989-1999.
[44]Li Z. Global synchronization of general delayed dynamical networks [J]. Chinese Physics Letters, 2007,24:1869-1872.
[45]罗群,吴薇,李丽香等.节点含时滞的不确定复杂网络的自适应同步研究[J].物理学报,2008,57(3)：1529-1534.
[46]Yan G, Zhou T, Hu B, Fu ZH Q, Wang B H. Efficient Routing on Complex Networks[J]. Phys. Rev. E, 2006,73(4):046108.
[47]Yang H X, Wang W X, Wu Z X, Wang B H. Traffic dynamics in scale-free networks with limited packet-delivering capacity[J].Physica A,2008,387:6857-6862.
[48]Cai S M, Yan G, Zhou T, et al. Scaling behaviors of an artificial traffic model on scale-free networks [J].Physics Letters A,2007,366:14-19.
[49]Gao Z Y, Li K P. Evolution of traffic flow with scale free topology Chin[J].Phys. Lett,2005,22:2711-2714.
[50]Wu J J, Gao Z Y, Sun H J, Huang H J. Congestion in different topologies of traffic networks[J]. Europhysics Letters,2006,74(3):560.
[51]Wu J J, Gao Z Y, Sun H J. Model for dynamic traffic congestion in scale-free networks[J]. Europhysics Letters,2006,76:787-793.
[52]Zhao X M, Gao Z Y. Topological effects on the performance of transportation networks Chin[J]. physics Letters,2007,24:283-286.
[53]Wang W X, Wang B H, Yin C Y, et al. Traffic dynamics based on local routing protocol on scale-free networks[J].Phys. Rev. E,2006,73(2):026111(7).
[54]Wang W X, Yin C Y, Yan G, Wang B H. Integrating local static and dynamic information for routing traffic [J]. Phys. Rev. E,2006,74:016101(5).
[55]Yin C Y, Wang B H, Wang W X, et al. Efficient routing on scale free networks based on local information [J]. Phys. Lett. A,2006,351:220-224.
[56]Wang B H, Zhou T. Traffic Flow and Efficient Routing on Scale-free Networks:A Survey [J]. Korean Physical Society,2007,50:134-141.
[57]Wang B H, Wang W X. Routing strategies in traffic network and phase transition in network traffic flow[J]. Physics and astronomy,2008,71:353-358.
[58]Liu Z H, Ma W C, Zhang H, Y, et al. An efficient approach of controlling traffic congestion in scale free networks[J]. Physica A,2006,370:843-853.
[59]Anthony Wren. General Review of the Use of Computers in Scheduling buses and Crews[A].In Computer Scheduling of Public Transport[C]. North. Holland Publishing Company.1981:3.16.
[60]Li Y H, Wu F J. Real-Time Scheduling on a Transit Bus Route [A]. In Computer Scheduling of Public Transport[C].Springer.Verlag,1992:213-235.
[61]Peter G F. Alternating Deadheading in Bus Route Operation [J].Transportation Science,1985, 19(1):13-28.
[62]Ceder A. Methods of creating bus timetables [J]. Transport Part A,1986,21:59-83.
[63]Christopher J E, Emilson C D S. British Bus Deregulation:Competition and Demand Coordination [J]. Journal of Urban Economics,1998,43:336-361.
[64]Dessouky M, Hall R, Nowroozi A, Mourikas K. Bus dispatching at timed transfer transit stations using bus tracking [J].Transportation Research Part C,1999,7(4):187-208.
[65]Palma A D, Lindsey R. Optimal Timetables for Public Transportation [J].Transportation Research Part B,2001,35:789-813.
[66]Ceder A, Golany B, Tal O. Creating bus timetableas with maximal Synchronization [J].Transp Ortation Research Part A,2001,35:913-928.
[67]Haghani A, Banihashemi M. Heuristic approaches of solving large-scale bus transit vehicle scheduling problem with route time constraints[J].Transportation Research Part A,2002,36(4):309-333.
[68]Maikol M, Rodrigues, Cid C, de Souza, Arnaldo V M. Vehicle and crew scheduling for urban bus lines [J]. European Journal of Operational,2006,170:844-862.
[69]Li J Q, Larry K. HeadSustainability provisions in the bus scheduling problem [J].Transportation Research Part D,2009,14:50-60.
[71]Blais J Y, Rousseau J M. Overview of HASTUS current and Future Versions [A].In Computer Transit Scheduling[C].Springer. Verlag,1988:175-187.
[72]Ceder A, Stern H. OPTIBUS:A Scheduling Package [A].In Computer Transit Scheduling [C] Springer. Verlag,1988:212-225.
[73]蒋光震,何显慈.公共交通线路组合调度模型[J].系统工程.1985,3(2)：51-59.
[74]孙芙灵.公交调度以及优化系统的研究与开发[D].(硕士学位论文).西安：西安公路交通大学,1998.
[75]孙芙灵.公交调度中发车间隔的确定方法的探讨[J].西安公路交通大学学报,1997,17(2)：44-48.
[76]刘云,梁文静,宋钦.北京市公交智能调度系统的网络设计及性能分析[J].北方交通大学学报,1999,23(5)：26-30.
[77]杨新苗,王炜.基于准实时信息的公交调度优化系统[J].交通与计算,2000,18(5)：12-15.
[78]董强,刘超慧等.公交车调度问题的研究[J].工程数学学报,2002,19(F02)：59-66.
[79]张飞舟.公交车辆智能调度及相关技术研究[D].(博士学位论文).北京：北京航空航天大学,2000.
[80]童刚.公交调度模型及算法[J].青岛科技大学学报,2004,25(3)：253-257.
[81]Liu Z G, Shen J S. Regional Bus Operation Bi-lever Programming Model Integrating Timetabling and Vehicle Scheduling [J]. Systerms Engineering-Theory and Practice,2007,27(11):135-141.
[82]Liu Z G, Shen J S, Wang H X, Yang W. Regional Bus Timetabling Model with Synchronization.[J]. Journal of Transportation Systems Engineering and Information Technology,2007,7(2):109-113.
[83]吴金闪,狄增如.从统计物理学对复杂网络研究[J].物理学进展,2004,24(1)：18-46.
[84]Wang X F. Complex networks:topology, dynamics and synchronization [J].International Journal of Bifurcation and Chaos,2002,12(5):885-916.
[85]Erdos P, Renyi A. On the evolution of random graphs [J]. Publ. Math. Inst. Hung. Acad. Sci., 1960,5:33-36.
[86]Watts D J, Strogatz S H. Collective dynamics of "small world" networks[J]. Nature,1998,393: 440-442.
[87]Newman M E J, Watts D J. Renormalization group analysis of the small-world network model [J]. Phys. Lett. A,1999,263:341-346.
[88]Barrat A, Weigt M. On the properties of small-world networks [J]. Eur. Phys. J. B,2000,13:547-560.
[89]Newman M E J, Moore C, Watts D J. Mean field solution of the small-world network model [J]. Phys. Rev. Lett,2000,84:3201-3204.
[90]Newman M E J. The structure and function of networks [J]. Computer Physics Communications,2002, 40-45.
[91]Pecora L M, Carroll T L. Master stability functions for synchronized coupled systems[J]. Phys. Rev. Lett,1998,80:2109-2112.
[92]Barahona M, Pecora L M. Synchronization in small-world systems[J]. Phys. Rev. Lett,2004,89(5): 054101.
[93]Li C G, Chen G R. Synchronization in general complex dynamical networks with coupling delays [J].Physica A,2004,43:236-278.
[94]Wang Q Y, Chen G R, Lu Q S, et al. Novel criteria of synchronization stability in complex networks with coupling delays [J]. Physica A,2007,378:527-536.
[95]Zhou J, Chen T P. Synchronization in general complex delayed dynamical networks [J].IEEE Trans. Circuits. Syst. I,2006,53:733-744.
[96]Masoller C, Mart A C, Zanette D H. Synchronization in an array of globally coupled maps with delayed interactions[J]. Physica A,2003,325:186-191.
[97]Cao J D, Lu J H. Adaptive synchronization of neural networks with or without time-varying delay [J]. Chaos,2006,16:013133.
[98]Albert R, Barabasi A L. Statistical mechanics of complex networks [J]. Rev.Mod.Phys,2002,74(1): 47-97.
[99]Strogatz S H. Exploring complex networks[J].Nature,2001,410:268-276.
[100]Park K, Lai Y C. Jamming in Complex Gradient Networks[J].Physical Review E,2005,71(6): 065105.
[101]Qian X L, Liu W Q,Yang J Z. Chinese Physics Letters,2006,23(4):790-793.
[102]吴晔,肖井华,占萌.强耦合混沌系统中的近似同步,物理学报,2007,56(9)：5119-5123.
[103]Wu Y, Liu W Q, Xiao J H, et al. Phys. Lett. A,2007,369:464-468.
[104]Moreno Y, Gomez J B, Pacheco A F. Instability of Scale-free Networks under Node-breaking Avalanches [EB/OL]. [2007.10.27]. http://arxiv.org/abs/cond.mat/0106136.
[105]Moreno Y, Pastor-Satorras R, Vazquez A, et al. Critical Load and Congestion Instabilities in Scale-free Networks [EB/OL].[2007.10.27]. http://arxiv.org/abs/cond.mat/0209474v1.
[106]Buzna L, Peters K, Helbing D. Modeling the Dynamics of Disaster Spreading in networks[J]. Physica A,2006,363:132-140.
[107]Latora V, Marchiori M. Efficient Behavior of Small-World Networks [J]. Physical Review,2001, 87(1):198701.
[108]Latora V, Marchiori M. Economic Small-world Behavior in Weighted Networks[J]. Eur. Phys. J. B,2003,32(2):249-263.
[109]翁文国,倪顺江,申世飞等.复杂网络上灾害蔓延动力学研究[J].物理学报,2007,56(4)：19：38-1943.
[110]Latora V, Marchiori M. Efficient behavior of small-world network[J].Physical Review Letters, 2001,87:198701.
[111]吴建军,高自友,孙会君,赵晖.城市交通系统复杂性—复杂网络方法及其应用[M].北京：科学出版社.2010.
[112]Albert R, Jeong H, Barabasi A L. Error and attack tolerance of complex networks[J]. Nature,2000, 406:378-382.
[113]Ahuja R K, Magnati T L, Orlin J B. Network Flows:Theory, Theory and Applications[M].Prent Ions. Hall. Englewood Cliffs, NJ,1993.
[114]Li C G, Chen G R. Synchronization in general complex dynamical networks with coupling delays[J]. Physical A,2004,343:236-278.
[115]Deigado J. Emergence of social conventions in complex networks[J].Artificial Intelligence, 2002,141(1.2):171-185.
[116]Barrat A, Barthelemy M, Vespignani A. Dynamical processes on Complex Networks[M]. Cambridge University Press,2008.
[117]Fortunato S. Damage spreading and opinion dynamics on scale-free networks[J]. Physical A,2005, 348:683-690.
[118]Moreno Y, Nekovee M, paeheeo A F. Dynamics of Rumor Spreading in Complex Networks[J]. Phys.Rev.E,2004,69:06613.
[119]Motter A E. Casade control and defense in complex networks[J]. Phys.Rev.Lett.,2004,93(9): 098701.
[120]Bakke H, Hansen A, Kertesz J. Failures and avalanches in complex networks[J]. Europhys. Lett., 2006,76:717-723.
[121]Crucitti P, Latora V, Marehiori M. Model for cascading failures in complex networks[J]. Phys.Rev.E, 2004,69(4):045104.
[122]Sorrentino F, Ott E. Adaptive Synehronization of Dynamics on Evolving Complex Networks[J]. Phys.Rev.Lett.,2008,100(11):114101.
[123]Gross T, Sayama H. Adaptive Networks:Theory, Models, and Applications[M]. Heidelberg, Springer Verlag,2009
[124]Gross T. Kevrekidis I G. Robust oscillations in SIS epidemics on adaptive networks:Coarse graining by automated moment closure[J]. Europhysics Lett,2008,82:38004.6.
[125]Gross T, Blasius B. Adaptive coevolutionary networks:a review Journal of the Royal Society[J]. Interface2008,5:259-271.
[126]Gross T, Lima C D, Blasius B. Epidemic dynamics on an adaptive network[J]. Phys.Rev.Lett,2006, 96:208701(4).
[127]Yu X L,Wallace K,Chen G R. Generating hyper chaos via state feedback control[J].lnt J Bifurcat Chaos,2005,15:3367-3375.
[128]Rossler O E. An equation for continuous chaos[J]. Phys.Lett.A,1976,57:397-398.
[129]WWW.JNBUS.COM.CN
[130]WWW.21ITS.COM
[131]Furth P G, Wilson N H N. Setting frequencies on bus routes:theory and practice[J]. Transportation research record 818, Transportation Research Board,Washington, D.C,1981:1-7.
[132]Ceder A, Stern H I. Optimal transit timetables for a fixed vehicle fleet[R].Proceedings of the Ninth Internatiaonal symposium On transportation and traffic theory,1984:331-355.
[133]Ceder A, Tal O. Timetable synchronization for bused Computer-aided scheduling of Public transport [M].Springer, NewYork.1999:245-258.
[134]KousoPoulos H N, Odoni A, Wilson N H M. Determination of headways as function of time varying characteristics on a transit network[J]. Computer scheduling of Public transport2,1985:192-220.
[135]Zolfaghari S, Azizi N, Mohamad Y J. A model for holding strategy in public transit systems with real-time information [J]. International Journal of Transport Management 2004,2:99-110.
[136]Fu L P, liu Q, Calamai P. Real Time Optimization Model for Dynamic Scheduling of Transit Operations [J]. Transportation research Record,2003,1857:48-55.
[137]Shrivastava P, Mohony M O. A model for development of optimized feeder routes and coordinated schedules a genetic algorithms approach [J].Transportation policy.2006,13:413-425.
[138]杨晓光.先进的公共汽车交通优先系统结构研究[A].中国城市交通规划学术委员会成立二十周年纪念论文集[C].北京：中国地质出版社,1999.
[139]戴英姿.快速公交(BRT)系统的交叉口优化控制与设计[D].(硕士学位论文).成都：西南交大,2005.
[140]徐康明,解建华,玛浚.快速公交车站运营模式的优势与效益分析[J].城市交通,2006(6),29-33.
[141]胡红,杨孝宽,魏中华等.基于成本效益优化的BRT规划方案评价研究[J].北京工业大学学报,2007(4)：393-397.
[142]高洋,李丽香,彭海朋,杨以先等.多重边融合复杂动态网络的自适应同步[J].物理学报2008,57(04)：2081-2091.
[143]罗群,高雅,齐雅楠,等.融合复杂动态网络的模型参考自适应同步研究[J].2009,58(10)：6809-6817.
[144]Niu H M. A Combination Transit Scheduling Model with Express Strategy Using Genetic Algorithm, American Society of Civil Engineering. ICTTS,2008,532-539.
[2]王炜,杨新苗,陈学武.城市公共交通系统规划方法与管理技术[M].北京：科学出版社,2002.
[3]Strogatz S H. Exploring complex networks[J]. Nature,2001,410:268-276.
[4]Barabasi A L, Albert R. Emergence of scaling in random networks[J]. Science,1999,286:509-512.
[5]Barabasi A L, Albert R, Jeong H. Mean-field theory for scale-free random networks[J]. Physical A, 1999,272:173-187.
[6]Watts D J, Strogatz S H. Collective dynamical of'small-world' networks[J]. Nature,1998,393: 440-442.
[7]Jeong H, Tombor B, Albert R, Oltvai Z, Barabasi A L. The large-scale organization of metabolic networks[J]. Nature,2000,407:651-654.
[8]Jin C W, Marsden I, Chen X Q, Liao X B. Dynamic DNA contacts observed in the NMR structure of winged Helix Protein-DNA Complex[J].Molecular Biology,1999,289:683-690.
[9]Newman M E J. The structure and functions of complex networks[J]. SIAM Rev,2003,45:167-256.
[10]Lu J H, Yu X H, Chen G R. Chaos synchronization of general complex dynamical networks[J]. Physica A,2004,334:281-302.
[11]Wang X F, Chen G R. Synchronization in small-word dynamical networks[J]. Int. J. Bifur. Chaos 2002,12(1):187-192.
[12]Wang X F, Chen G R. Synchronization in scale-free dynamical networks:Robustness and fragilityfJ]. IEEE Trans. Circuits and Systems,2002,49 (1):54-62.
[13]Hong H, Choi M Y, Kim B J. Synchronization on small-world networks[J]. Phys. Rev. E, 2002,65(2):026139(5).
[14]Barahona M, Pecora L M. Synchronization in small-world systems[J]. Phys. Rev. Lett.,2002,89(5): 054101.
[15]Lu J H, Yu X H, Chen G R, Cheng D Z. Characterizing the synchronizability of small-world dynamical networks[J]. IEEE Trans.Circuits and Systems,2004,51(4):787-796.
[16]冯存芳.时滞混沌系统的同步及复杂网络上的动力学行为[D].博士学位论文,兰州：兰州大学,2009.
[17]赵明.复杂网络上动力系统同步现象[D].(博士学位论文).合肥：中国科学技术大学,2007.
[18]戴杨.耦合时滞复杂网络的同步性研究[D].(博士学位论文).上海：上海交通大学,2009.
[19]钱伟.时滞系统的若干问题的研究[D].(博士学位论文).杭州：浙江大学,2009.
[20]赵跃辉.带有时变时滞的复杂动态网络的同步准则[D].(硕士学位论文).武汉：武汉理工大学,2009.
[21]张好智.城市交通网络设计问题的相关优化模型与算法[D].(博士学位论文).北京：北京交通大学,2007.
[22]Lu W L, Chen T P. Synchronization of coupled connected neural networks with delays [J]. IEEE Transactions on Circuits and Systems I,2004,51(12):2491-2503.
[23]Lu J H, Chen G R. A new chaotic attractor coined. International Journal of Bifurcation and Chaos [J],2002,12(3):659-661.
[24]Wu J S, Jiao L C. Synchronization in complex delayed dynamical networks with nonsymmetric coupling [J]. Physica A,2007,386:513-530.
[25]Wu X. Synchronization based topology identification of weighted general complex dynamical networks with time-varying coupling delay [J]. Physica A,2008,387:997-1008.
[26]Yu W W, Cao J D. Adaptive Q-S (lag. anticipated, and complete) time-varying synchronization and parameters identification of uncertain delayed neural networks[J]. Chaos,2006,16:023119.
[27]Yu W W, Cao J D. Adaptive synchronization and lag synchronization of uncertain dynamical system with time delay based on parameter identification[J]. Physica A,2007,375(2):467-482.
[28]Zhou J, Xiang L, Liu Z R. Global synchronization in general complex delayed dynamical networks and its applications[J]. IEEE Transactions on Automatic Control,2007,385(2):729-742.
[29]Cai S M, Zhou J, Xiang L, Liu Z R. Robust impulsive synchronization of complex delayed dynamical networks[J]. Physics Letters A,2008,372(30):4990-4995.
[30]Li C G, Chen G R. Synchronization in general complex dynamical networks with coupling delays[J]. Physica A,2004,343:263-278.
[31]Gao H J, Lam J, Chen G R. New criteria for synchronization stability of general complex dynamical networks with coupling delays[J]. Physics Letters A,2006,360:263-273.
[32]Wu J S, Jiao L C. Synchronization in dynamic networks with nonsymmetrical time-delay coupling based on linear feedback controllers [J].Physica A:Statistical Mechanics and its Applications,2008,387 (8-9):2111-2119.
[33]Zhou J, Lu J A, Lii J H. Adaptive synchronization of an uncertain complex dynamical network[J]. Physica A,2006,51(4):652-656.
[34]Zhou J, Chen T P. Synchronization in general complex delayed dynamical networks[J]. IEEE Transactions on Circuits and Systems-I:Regular Papers,2006,53(3):733-744.
[35]Zhou J, Xiang L, Liu Z R. Synchronization in complex delayed dynamical networks with impulsive effects[J]. Physica A,2007,384(2):684-692.
[36]Wang Q Y, Duan Z S, Chen G R, Feng Z S. Synchronization in a class of weighted complex networks with coupling delays[J]. Physica A:Statistical Mechanics and its Applications,2008,387(22):5616-5622.
[37]Xiang L Y, Liu Z X, Chen Z Q. Pinning control of complex dynamical networks with general topology[J]. Physica A,2007,379(1):298-306.
[38]Li C P, Sun W G, Kurths J. Synchronization of complex dynamical networks with time delays [J]. Physia A,2006,361:24-34.
[39]Wang L, Dai H p, Dong H, et al. Adaptive synchronization of weighted complex dynamical networks with coupling time-varying delays [J]. Physics Letters A,2008,372:3632-3639.
[40]Zheng S, Bi Q H, Cai G L. Adaptive projective synchronization in complex networks with time-varying coupling delay [J]. Physics Letters A,2009,373:1553-1559.
[41]Koo J H, Ji D H, Won S C. Synchronization of singular complex dynamical networks with time-varying delays [J]. Applied Mathematics and Computation,2010,217(8):3916-3923.
[42]Tang Y, Fang J A, Xia M, et al. Synchronization of Takagi-Sugeno fuzzy stochastic discrete-time complex networks with mixed time varying delays [J].Applied Mathematical Modelling,2010,34:843-855.
[43]Zuo Z Q, Yang C L, Wang Y J. A unified framework of exponential synchronization for complex networks with time-varying delays [J]. Physics Letters A,2010,374:1989-1999.
[44]Li Z. Global synchronization of general delayed dynamical networks [J]. Chinese Physics Letters, 2007,24:1869-1872.
[45]罗群,吴薇,李丽香等.节点含时滞的不确定复杂网络的自适应同步研究[J].物理学报,2008,57(3)：1529-1534.
[46]Yan G, Zhou T, Hu B, Fu ZH Q, Wang B H. Efficient Routing on Complex Networks[J]. Phys. Rev. E, 2006,73(4):046108.
[47]Yang H X, Wang W X, Wu Z X, Wang B H. Traffic dynamics in scale-free networks with limited packet-delivering capacity[J].Physica A,2008,387:6857-6862.
[48]Cai S M, Yan G, Zhou T, et al. Scaling behaviors of an artificial traffic model on scale-free networks [J].Physics Letters A,2007,366:14-19.
[49]Gao Z Y, Li K P. Evolution of traffic flow with scale free topology Chin[J].Phys. Lett,2005,22:2711-2714.
[50]Wu J J, Gao Z Y, Sun H J, Huang H J. Congestion in different topologies of traffic networks[J]. Europhysics Letters,2006,74(3):560.
[51]Wu J J, Gao Z Y, Sun H J. Model for dynamic traffic congestion in scale-free networks[J]. Europhysics Letters,2006,76:787-793.
[52]Zhao X M, Gao Z Y. Topological effects on the performance of transportation networks Chin[J]. physics Letters,2007,24:283-286.
[53]Wang W X, Wang B H, Yin C Y, et al. Traffic dynamics based on local routing protocol on scale-free networks[J].Phys. Rev. E,2006,73(2):026111(7).
[54]Wang W X, Yin C Y, Yan G, Wang B H. Integrating local static and dynamic information for routing traffic [J]. Phys. Rev. E,2006,74:016101(5).
[55]Yin C Y, Wang B H, Wang W X, et al. Efficient routing on scale free networks based on local information [J]. Phys. Lett. A,2006,351:220-224.
[56]Wang B H, Zhou T. Traffic Flow and Efficient Routing on Scale-free Networks:A Survey [J]. Korean Physical Society,2007,50:134-141.
[57]Wang B H, Wang W X. Routing strategies in traffic network and phase transition in network traffic flow[J]. Physics and astronomy,2008,71:353-358.
[58]Liu Z H, Ma W C, Zhang H, Y, et al. An efficient approach of controlling traffic congestion in scale free networks[J]. Physica A,2006,370:843-853.
[59]Anthony Wren. General Review of the Use of Computers in Scheduling buses and Crews[A].In Computer Scheduling of Public Transport[C]. North. Holland Publishing Company.1981:3.16.
[60]Li Y H, Wu F J. Real-Time Scheduling on a Transit Bus Route [A]. In Computer Scheduling of Public Transport[C].Springer.Verlag,1992:213-235.
[61]Peter G F. Alternating Deadheading in Bus Route Operation [J].Transportation Science,1985, 19(1):13-28.
[62]Ceder A. Methods of creating bus timetables [J]. Transport Part A,1986,21:59-83.
[63]Christopher J E, Emilson C D S. British Bus Deregulation:Competition and Demand Coordination [J]. Journal of Urban Economics,1998,43:336-361.
[64]Dessouky M, Hall R, Nowroozi A, Mourikas K. Bus dispatching at timed transfer transit stations using bus tracking [J].Transportation Research Part C,1999,7(4):187-208.
[65]Palma A D, Lindsey R. Optimal Timetables for Public Transportation [J].Transportation Research Part B,2001,35:789-813.
[66]Ceder A, Golany B, Tal O. Creating bus timetableas with maximal Synchronization [J].Transp Ortation Research Part A,2001,35:913-928.
[67]Haghani A, Banihashemi M. Heuristic approaches of solving large-scale bus transit vehicle scheduling problem with route time constraints[J].Transportation Research Part A,2002,36(4):309-333.
[68]Maikol M, Rodrigues, Cid C, de Souza, Arnaldo V M. Vehicle and crew scheduling for urban bus lines [J]. European Journal of Operational,2006,170:844-862.
[69]Li J Q, Larry K. HeadSustainability provisions in the bus scheduling problem [J].Transportation Research Part D,2009,14:50-60.
[71]Blais J Y, Rousseau J M. Overview of HASTUS current and Future Versions [A].In Computer Transit Scheduling[C].Springer. Verlag,1988:175-187.
[72]Ceder A, Stern H. OPTIBUS:A Scheduling Package [A].In Computer Transit Scheduling [C] Springer. Verlag,1988:212-225.
[73]蒋光震,何显慈.公共交通线路组合调度模型[J].系统工程.1985,3(2)：51-59.
[74]孙芙灵.公交调度以及优化系统的研究与开发[D].(硕士学位论文).西安：西安公路交通大学,1998.
[75]孙芙灵.公交调度中发车间隔的确定方法的探讨[J].西安公路交通大学学报,1997,17(2)：44-48.
[76]刘云,梁文静,宋钦.北京市公交智能调度系统的网络设计及性能分析[J].北方交通大学学报,1999,23(5)：26-30.
[77]杨新苗,王炜.基于准实时信息的公交调度优化系统[J].交通与计算,2000,18(5)：12-15.
[78]董强,刘超慧等.公交车调度问题的研究[J].工程数学学报,2002,19(F02)：59-66.
[79]张飞舟.公交车辆智能调度及相关技术研究[D].(博士学位论文).北京：北京航空航天大学,2000.
[80]童刚.公交调度模型及算法[J].青岛科技大学学报,2004,25(3)：253-257.
[81]Liu Z G, Shen J S. Regional Bus Operation Bi-lever Programming Model Integrating Timetabling and Vehicle Scheduling [J]. Systerms Engineering-Theory and Practice,2007,27(11):135-141.
[82]Liu Z G, Shen J S, Wang H X, Yang W. Regional Bus Timetabling Model with Synchronization.[J]. Journal of Transportation Systems Engineering and Information Technology,2007,7(2):109-113.
[83]吴金闪,狄增如.从统计物理学对复杂网络研究[J].物理学进展,2004,24(1)：18-46.
[84]Wang X F. Complex networks:topology, dynamics and synchronization [J].International Journal of Bifurcation and Chaos,2002,12(5):885-916.
[85]Erdos P, Renyi A. On the evolution of random graphs [J]. Publ. Math. Inst. Hung. Acad. Sci., 1960,5:33-36.
[86]Watts D J, Strogatz S H. Collective dynamics of "small world" networks[J]. Nature,1998,393: 440-442.
[87]Newman M E J, Watts D J. Renormalization group analysis of the small-world network model [J]. Phys. Lett. A,1999,263:341-346.
[88]Barrat A, Weigt M. On the properties of small-world networks [J]. Eur. Phys. J. B,2000,13:547-560.
[89]Newman M E J, Moore C, Watts D J. Mean field solution of the small-world network model [J]. Phys. Rev. Lett,2000,84:3201-3204.
[90]Newman M E J. The structure and function of networks [J]. Computer Physics Communications,2002, 40-45.
[91]Pecora L M, Carroll T L. Master stability functions for synchronized coupled systems[J]. Phys. Rev. Lett,1998,80:2109-2112.
[92]Barahona M, Pecora L M. Synchronization in small-world systems[J]. Phys. Rev. Lett,2004,89(5): 054101.
[93]Li C G, Chen G R. Synchronization in general complex dynamical networks with coupling delays [J].Physica A,2004,43:236-278.
[94]Wang Q Y, Chen G R, Lu Q S, et al. Novel criteria of synchronization stability in complex networks with coupling delays [J]. Physica A,2007,378:527-536.
[95]Zhou J, Chen T P. Synchronization in general complex delayed dynamical networks [J].IEEE Trans. Circuits. Syst. I,2006,53:733-744.
[96]Masoller C, Mart A C, Zanette D H. Synchronization in an array of globally coupled maps with delayed interactions[J]. Physica A,2003,325:186-191.
[97]Cao J D, Lu J H. Adaptive synchronization of neural networks with or without time-varying delay [J]. Chaos,2006,16:013133.
[98]Albert R, Barabasi A L. Statistical mechanics of complex networks [J]. Rev.Mod.Phys,2002,74(1): 47-97.
[99]Strogatz S H. Exploring complex networks[J].Nature,2001,410:268-276.
[100]Park K, Lai Y C. Jamming in Complex Gradient Networks[J].Physical Review E,2005,71(6): 065105.
[101]Qian X L, Liu W Q,Yang J Z. Chinese Physics Letters,2006,23(4):790-793.
[102]吴晔,肖井华,占萌.强耦合混沌系统中的近似同步,物理学报,2007,56(9)：5119-5123.
[103]Wu Y, Liu W Q, Xiao J H, et al. Phys. Lett. A,2007,369:464-468.
[104]Moreno Y, Gomez J B, Pacheco A F. Instability of Scale-free Networks under Node-breaking Avalanches [EB/OL]. [2007.10.27]. http://arxiv.org/abs/cond.mat/0106136.
[105]Moreno Y, Pastor-Satorras R, Vazquez A, et al. Critical Load and Congestion Instabilities in Scale-free Networks [EB/OL].[2007.10.27]. http://arxiv.org/abs/cond.mat/0209474v1.
[106]Buzna L, Peters K, Helbing D. Modeling the Dynamics of Disaster Spreading in networks[J]. Physica A,2006,363:132-140.
[107]Latora V, Marchiori M. Efficient Behavior of Small-World Networks [J]. Physical Review,2001, 87(1):198701.
[108]Latora V, Marchiori M. Economic Small-world Behavior in Weighted Networks[J]. Eur. Phys. J. B,2003,32(2):249-263.
[109]翁文国,倪顺江,申世飞等.复杂网络上灾害蔓延动力学研究[J].物理学报,2007,56(4)：19：38-1943.
[110]Latora V, Marchiori M. Efficient behavior of small-world network[J].Physical Review Letters, 2001,87:198701.
[111]吴建军,高自友,孙会君,赵晖.城市交通系统复杂性—复杂网络方法及其应用[M].北京：科学出版社.2010.
[112]Albert R, Jeong H, Barabasi A L. Error and attack tolerance of complex networks[J]. Nature,2000, 406:378-382.
[113]Ahuja R K, Magnati T L, Orlin J B. Network Flows:Theory, Theory and Applications[M].Prent Ions. Hall. Englewood Cliffs, NJ,1993.
[114]Li C G, Chen G R. Synchronization in general complex dynamical networks with coupling delays[J]. Physical A,2004,343:236-278.
[115]Deigado J. Emergence of social conventions in complex networks[J].Artificial Intelligence, 2002,141(1.2):171-185.
[116]Barrat A, Barthelemy M, Vespignani A. Dynamical processes on Complex Networks[M]. Cambridge University Press,2008.
[117]Fortunato S. Damage spreading and opinion dynamics on scale-free networks[J]. Physical A,2005, 348:683-690.
[118]Moreno Y, Nekovee M, paeheeo A F. Dynamics of Rumor Spreading in Complex Networks[J]. Phys.Rev.E,2004,69:06613.
[119]Motter A E. Casade control and defense in complex networks[J]. Phys.Rev.Lett.,2004,93(9): 098701.
[120]Bakke H, Hansen A, Kertesz J. Failures and avalanches in complex networks[J]. Europhys. Lett., 2006,76:717-723.
[121]Crucitti P, Latora V, Marehiori M. Model for cascading failures in complex networks[J]. Phys.Rev.E, 2004,69(4):045104.
[122]Sorrentino F, Ott E. Adaptive Synehronization of Dynamics on Evolving Complex Networks[J]. Phys.Rev.Lett.,2008,100(11):114101.
[123]Gross T, Sayama H. Adaptive Networks:Theory, Models, and Applications[M]. Heidelberg, Springer Verlag,2009
[124]Gross T. Kevrekidis I G. Robust oscillations in SIS epidemics on adaptive networks:Coarse graining by automated moment closure[J]. Europhysics Lett,2008,82:38004.6.
[125]Gross T, Blasius B. Adaptive coevolutionary networks:a review Journal of the Royal Society[J]. Interface2008,5:259-271.
[126]Gross T, Lima C D, Blasius B. Epidemic dynamics on an adaptive network[J]. Phys.Rev.Lett,2006, 96:208701(4).
[127]Yu X L,Wallace K,Chen G R. Generating hyper chaos via state feedback control[J].lnt J Bifurcat Chaos,2005,15:3367-3375.
[128]Rossler O E. An equation for continuous chaos[J]. Phys.Lett.A,1976,57:397-398.
[129]WWW.JNBUS.COM.CN
[130]WWW.21ITS.COM
[131]Furth P G, Wilson N H N. Setting frequencies on bus routes:theory and practice[J]. Transportation research record 818, Transportation Research Board,Washington, D.C,1981:1-7.
[132]Ceder A, Stern H I. Optimal transit timetables for a fixed vehicle fleet[R].Proceedings of the Ninth Internatiaonal symposium On transportation and traffic theory,1984:331-355.
[133]Ceder A, Tal O. Timetable synchronization for bused Computer-aided scheduling of Public transport [M].Springer, NewYork.1999:245-258.
[134]KousoPoulos H N, Odoni A, Wilson N H M. Determination of headways as function of time varying characteristics on a transit network[J]. Computer scheduling of Public transport2,1985:192-220.
[135]Zolfaghari S, Azizi N, Mohamad Y J. A model for holding strategy in public transit systems with real-time information [J]. International Journal of Transport Management 2004,2:99-110.
[136]Fu L P, liu Q, Calamai P. Real Time Optimization Model for Dynamic Scheduling of Transit Operations [J]. Transportation research Record,2003,1857:48-55.
[137]Shrivastava P, Mohony M O. A model for development of optimized feeder routes and coordinated schedules a genetic algorithms approach [J].Transportation policy.2006,13:413-425.
[138]杨晓光.先进的公共汽车交通优先系统结构研究[A].中国城市交通规划学术委员会成立二十周年纪念论文集[C].北京：中国地质出版社,1999.
[139]戴英姿.快速公交(BRT)系统的交叉口优化控制与设计[D].(硕士学位论文).成都：西南交大,2005.
[140]徐康明,解建华,玛浚.快速公交车站运营模式的优势与效益分析[J].城市交通,2006(6),29-33.
[141]胡红,杨孝宽,魏中华等.基于成本效益优化的BRT规划方案评价研究[J].北京工业大学学报,2007(4)：393-397.
[142]高洋,李丽香,彭海朋,杨以先等.多重边融合复杂动态网络的自适应同步[J].物理学报2008,57(04)：2081-2091.
[143]罗群,高雅,齐雅楠,等.融合复杂动态网络的模型参考自适应同步研究[J].2009,58(10)：6809-6817.
[144]Niu H M. A Combination Transit Scheduling Model with Express Strategy Using Genetic Algorithm, American Society of Civil Engineering. ICTTS,2008,532-539.