基于复杂适应系统理论的社会经济系统建模与仿真研究
|
摘要
社会经济系统、生态系统、制造系统等复杂巨系统由于其内部高度的非线性、关联性和分散性,使得传统的数理方法无力解决这类系统宏观上涌现的整体结构与行为。复杂性科学旨在从整体上把握系统的结构与行为,抛弃了还原论思想,自下而上地研究其集体涌现行为。20世纪90年代,圣菲研究所提出的复杂适应系统理论成为当代复杂性科学的理论基础,其方法论——基于Agent的建模方法——大大方便了社会科学工作者对社会系统进行实验与分析,有助于理解社会经济系统的运行。
本文首先对复杂性科学和复杂系统理论进行了简要回顾,概述了其主要理论分支与研究方法,给出了一个研究大背景。并着重介绍了复杂适应系统(Complex Adaptive Systems, CAS)理论及基于Agent的建模方法(Agent Based Modeling, ABM),分析了它们在社会经济系统的应用前景与研究思路。
针对社会经济系统的一些现象,本文将CAS理论应用于社会经济系统,并分别分别给出了三个应用实例。第一个实例是人工经济模型,在虚拟世界中构造一个由适应性Agent组成的经济系统,Agent之间进行着交易与学习,交易网络和资源传播网络以“无标度”的拓扑形式涌现出来,在市场中少数交易者控制着大部分的交易。第二个实例解释了自私的企业为何会自发的涌现出对社会的责任,通过对企业建立广义Lotka-Volterra模型构建了系统的多Agent模型,发现自私的企业通过相互之间的竞争而逐渐地开始采纳“利他的”企业社会责任这一行业规范。第三个实例以社会系统中的传播现象为对象,分别研究了小世界上的简单传播,复杂传播和多元文化传播。研究结果表明,不同类型的传播在小世界拓扑结构的社会网络上表现出了完全不同的行为,复杂传播会因加边概率的增加而减小传播成功的几率,但传播速度会显著地增加;而多元文化传播的研究则显示全局上文化的沟通不但不会促进不同文化集团之间的融合,反而会加剧他们间的对立,这一结果能加深对全球化和文化间的冲突的理解。
本文最后还对多Agent仿真平台进行了介绍,本文从理论到方法到应用全方位的对复杂适应系统及其方法论——基于Agent的建模方法——进行了论述。复杂适应系统理论提供了一个全新的视角,其系统的层次性,非线性、涌现性以及分化性等复杂系统特征在一定程度上弥补了传统社会科学研究方法的不足。本文从理论到方法到应用全面的论述了复杂适应系统与基于Agent的建模方法在社会经济系统中的实践,为更深层次的工作起到铺垫作用。
Due to the inherent nonlinearity, coupling and distributedness of Complex Social Systems, the traditional mathematical methods are invalid to handle the emergent characteristics and macro behavior of the complex systems. Complexity Science aims to grasp the structure and behavior of large scale systems. It abandoned the traditional reductionism, which asserts that the nature of complex things is reduced to the nature of sums of simpler or more fundamental things. As a foundation of Complexity Science, Complex Adaptive Systems provides a metaphor to the operation of complex system and its methodology—the agent based modeling—facilitates the research and analysis of large-scale systems.
This paper traces back the history of complex system and complexity science to summarize the primary schools of system science and its research methods. Chapter 2 emphasizes the theory of Complex Adaptive Systems and the Agent Based Modeling methodology.
Based on the research background and the complex phenomena of social-economical system, three computer simulations were built to validate the application. First model is the Artificial Economy Model, which is a virtual world composed of numerous adaptive agents. The Scale free Transaction Network and propagation network emerge out of the local interations of adaptive agents. Second model explained how a bundle of selfish firms compete with each other to emerge an altruism Corporate Social Responsibility(CSR). This model is built on the generalized Lotka-Volterra model which is suitable for multi agent competing system. The third model is proposed to investigate the contagion process on the“small-world”social networks. Simple contagion, complex contagion and multi-dimensional culture disseminations are well explored. The results showed that more links or global interations introduced in the networked systems, more rigorous these culture groups opposed to each other! Globalization can not accelerate the understanding of different cultures but even to increase their gap!
The multi agent simulation platforms are introduced at the end of the thesis. The complex system characteristics, such a hierarchy, nonlinearity, emergence and differentiation and so on, got by its model offset the shortage of traditional economics research to a certain extent. This study is of active implication for the advanced application of the theory in China and could hopefully provide some experience technical support for future application of multi agent simulation technology.
本文首先对复杂性科学和复杂系统理论进行了简要回顾,概述了其主要理论分支与研究方法,给出了一个研究大背景。并着重介绍了复杂适应系统(Complex Adaptive Systems, CAS)理论及基于Agent的建模方法(Agent Based Modeling, ABM),分析了它们在社会经济系统的应用前景与研究思路。
针对社会经济系统的一些现象,本文将CAS理论应用于社会经济系统,并分别分别给出了三个应用实例。第一个实例是人工经济模型,在虚拟世界中构造一个由适应性Agent组成的经济系统,Agent之间进行着交易与学习,交易网络和资源传播网络以“无标度”的拓扑形式涌现出来,在市场中少数交易者控制着大部分的交易。第二个实例解释了自私的企业为何会自发的涌现出对社会的责任,通过对企业建立广义Lotka-Volterra模型构建了系统的多Agent模型,发现自私的企业通过相互之间的竞争而逐渐地开始采纳“利他的”企业社会责任这一行业规范。第三个实例以社会系统中的传播现象为对象,分别研究了小世界上的简单传播,复杂传播和多元文化传播。研究结果表明,不同类型的传播在小世界拓扑结构的社会网络上表现出了完全不同的行为,复杂传播会因加边概率的增加而减小传播成功的几率,但传播速度会显著地增加;而多元文化传播的研究则显示全局上文化的沟通不但不会促进不同文化集团之间的融合,反而会加剧他们间的对立,这一结果能加深对全球化和文化间的冲突的理解。
本文最后还对多Agent仿真平台进行了介绍,本文从理论到方法到应用全方位的对复杂适应系统及其方法论——基于Agent的建模方法——进行了论述。复杂适应系统理论提供了一个全新的视角,其系统的层次性,非线性、涌现性以及分化性等复杂系统特征在一定程度上弥补了传统社会科学研究方法的不足。本文从理论到方法到应用全面的论述了复杂适应系统与基于Agent的建模方法在社会经济系统中的实践,为更深层次的工作起到铺垫作用。
Due to the inherent nonlinearity, coupling and distributedness of Complex Social Systems, the traditional mathematical methods are invalid to handle the emergent characteristics and macro behavior of the complex systems. Complexity Science aims to grasp the structure and behavior of large scale systems. It abandoned the traditional reductionism, which asserts that the nature of complex things is reduced to the nature of sums of simpler or more fundamental things. As a foundation of Complexity Science, Complex Adaptive Systems provides a metaphor to the operation of complex system and its methodology—the agent based modeling—facilitates the research and analysis of large-scale systems.
This paper traces back the history of complex system and complexity science to summarize the primary schools of system science and its research methods. Chapter 2 emphasizes the theory of Complex Adaptive Systems and the Agent Based Modeling methodology.
Based on the research background and the complex phenomena of social-economical system, three computer simulations were built to validate the application. First model is the Artificial Economy Model, which is a virtual world composed of numerous adaptive agents. The Scale free Transaction Network and propagation network emerge out of the local interations of adaptive agents. Second model explained how a bundle of selfish firms compete with each other to emerge an altruism Corporate Social Responsibility(CSR). This model is built on the generalized Lotka-Volterra model which is suitable for multi agent competing system. The third model is proposed to investigate the contagion process on the“small-world”social networks. Simple contagion, complex contagion and multi-dimensional culture disseminations are well explored. The results showed that more links or global interations introduced in the networked systems, more rigorous these culture groups opposed to each other! Globalization can not accelerate the understanding of different cultures but even to increase their gap!
The multi agent simulation platforms are introduced at the end of the thesis. The complex system characteristics, such a hierarchy, nonlinearity, emergence and differentiation and so on, got by its model offset the shortage of traditional economics research to a certain extent. This study is of active implication for the advanced application of the theory in China and could hopefully provide some experience technical support for future application of multi agent simulation technology.
引文
[1]许国志编.系统科学.上海:上海科技教育出版社. 2000.9.
[2]魏宏森,宋永华等.开创复杂性研究的新学科——系统科学纵览.出版社:四川教育出版社. 1991年12月第1版.
[3]贝塔朗菲.一般系统论——基础,发展,应用.北京:社会科学文献出版社. 1987.
[4]维纳N.控制论.郝季仁译.北京:科学出版社. 1963.
[5]香农E.通信的数学理论.沈永朝译.北京:求实出版社. 1989. 508-600.
[6]尼克利斯G,普利高津I.非平衡系统的自组织.徐锡申等译.北京:科学出版社,1986.
[7]哈肯H.协同学引论.徐锡申等译.北京:原子能出版社. 1984.
[8]艾根M,舒斯特P.曾国屏、沈小峰译.超循环论.上海:上海译文出版社,1990.
[9] Neumann JV. Theory of Self-reproducing Automata. University of Illinois Press. 1966
[10]李建会,张江.数字创世纪:人工生命的新科学.北京:科学出版社.2005.12.
[11] S. Wolfram. Cellular Automata as Simple Self-Organizing Systems. Caltech preprint CALT-68-938, 1982.
[12]袁崇义. PETRI网原理.北京:电子工业出版社. 1998.4.
[13] Forrester JW. Industrial Dynamics. Cambridge: MIT Press, 1961.
[14] http://jasss.soc.surrey.ac.uk/JASSS.html
[15] Dianne CB. ASPEN-EE: An Agent-Based Model of Infrastructure Interdependency. Sandia Report 2000.
[16] Epstein JM, Axtell R. Growing Artificial Societies: Social Science from the Bottom up. Washington, D.C.: Brookings Institution Press. 1996.
[17]张江,基于Agent的计算经济学建模方法及其关键技术研究[D(]博士学位论文)2005
[18] Shi YR, Zhang J, Gao L and Zhou C. Scale-Free Networks Emerge out of Micro-Mechanism in an Agent-based Computational Economic Model
[19]约翰·霍兰著.周晓牧,韩晖译.隐秩序-适应性造就复杂性.上海科技教育出版社,2001.
[20] http://www.red3d.com/cwr/boids/
[21] Axelrod R. The Evolution of Cooperation. New York: Basic Books, 1984.
[22] Arthur B, et al. Asset Pricing Under Endogenous Expectations. Santa Fe Institute Paper, 1996.
[23]霍兰,陈禹等译.涌现--从混沌到秩序.上海:上海科学技术出版社. 2001.
[24]张江.基于Agent的计算经济学建模方法及其关键技术研究博士学位论文,北京交通大学.
[25]方美琪,张树人编著.复杂系统建模与仿真.北京:人民大学出版社. 2005.
[26] Howitt P, Clower R. The emergence of economic organization. Journal of Economic Behavior & Organization. Vol. 41. (2000): 55-84.
[27] Wilhite A. Bilateral Trade and‘Small-World’Networks. Computational Economics Vol. 18.(2001): 49–64.
[28] Pujol JM, Flache A, Delgado J and Sangüesa J, How Can Social Networks Ever Become Complex? Modelling the Emergence of Complex Networks from Local Social Exchanges. Journal of Artificial Societies and Social Simulation. vol. 8, no. 4 ( 2005 ) . http://jasss.soc.surrey.ac.uk/8/4/12.html
[29] Tesfatsion L. Agent-Based Computational Economics. ISU Economics Working Paper No. 1, Revised August 24, 2003.
[30] Schelling TC. Micromotives and Macrobehavior. W. W. Norton & Company, 1978.
[31] Kiyotaki N, Wright R. On money as a medium of exchange. Journal of Political Economy, 1989, vol 0(97): 927~954.
[32] Lane D: Artificial worlds and economics. Journal of Evolutionary Economics. 1992. vol 0(3): 89~107: 89~107.
[33] http://www.econ.iastate.edu/tesfatsi/ace.htm
[34] Gintis, H. Game theory evolving. Princeton, NJ: The Princeton University Press. 2000.
[35] Rust, J., Miller, J. H., and Palmer, R. Characterizing effective trading strategies: Insights from a computerized double auction tournament. Journal of Economic Dynamics and Control 1994. 18, 61–96.
[36] Gode, DK and Sunder, S. Allocative efficiency of markets with zero-intelligence traders: Market as a partial substitute for individual rationality [J]. Journal of Political Economy 1996. 101, 119–137.
[37] Vriend, NJ. Self-organization of markets: An example of a computational approach[J]. Computational Economics 1995. 8: 205–231.
[38] Edmonds B, Moss S. From KISS to KIDS-an "anti-simplistic" modeling approach. Davidsson Paul, Logan Brian et.al: Multi-Agent and Multi-Agent-Based Simulation: Joint Workshop MABS 2004 (Lecture Notes in Computer Science / Lecture Notes in Artificial Intelligence), Springer: 2005. 130-144
[39] Claudia PW, Ebenoth E. An Adaptive Toolbox Model: a pluralistic modelling approach for human behaviour based on observation. Journal of Artificial Societies and Social Simulation, vol. 7(1)http://jasss.soc.surrey.ac.uk/7/1/3.html
[40] Sun R. and Naveh I.Simulating Organizational Decision-Making Using a Cognitively Realistic Agent Model [J]. Journal of Artificial Societies and Social Simulation, 2004. vol. 7(3)http://jasss.soc.surrey.ac.uk/7/3/5.html
[41] Prietula, M. J., Carley, K. M., and Gasser, L. Simulating organizations: Computational models of institutions and groups [M]. Cambridge, MA: The MIT Press.
[42] Dawid, H, Reimann, M., and Bullnheimer, B. To innovate or not to innovate? IEEE Transactions on Evolutionary Computation 2001. 5: 471–481.
[43]张江,李学伟.用数字人工生命模型探索复杂适应系统,复杂系统与复杂性科学第2卷第1期2005年1月.
[44] Holland J, Genetic algorithms and Classifier Systems: Foundations and Future Directions. in Proceedings of the Second International Conference on Genetic Algorithms, Lawrence Erlbaum Associates, publishers, 1987, pp. 82-89.
[45]卢代富.国外企业社会责任界说评述.现代法学,2001 (6): 137-144.
[46]斯蒂芬p.罗宾斯管理学〔第四版〕.北京.中国人民大学出版社:1997年4月.
[47] Carroll, A. B. Corporate Social Responsibility: Evolution of a Definitional Construct [J]. Business and Society, 1999, 38(3): 268-295.
[48] Varleri Paone. Challenging Corporate Social Responsibility: The Emerging Factor. The fifth Asian Academy of Management Conference & AOM. Tokyo December 2006.
[49]陆征一周义仓.数学生物进展.科学出版社出版. 2006.4.
[50] Solomon S. Generalized Lotka-Volterra (GLV) Models and Generic Emergence of Scaling Laws in Stock Markets. in "Applications of Simulation to Social Sciences" ,Eds: G Ballot and G Weisbuch; Hermes Science Publications 2000.
[51] Faust,K.1994.Social Networks Analysis: Methods and Applications. Cambridge, England: Cambridge University Press.
[52] Watts J S, Strogatz S H. Collective dynamics of‘small-world’networks. Nature, 1998, 393: 440.
[53] Faloutsos M, Faloutsos P, Faloutsos C. On power-law relationships of the Internet topology. Computer Communications Review, 1999, 29: 251
[54] Sen P et al. Small-world properties of the Indian railway network. Phys. Rev. E, 2003, 67: 036106.
[55] Barabasi AL, Albert R. Emergence of scaling in random networks. Science, 1999, 286(5439):509~512.
[56] Jeong H, Mason SP, Barabási AL, Oltvai ZN. Lethality and centrality in protein networks NATURE. VOL 411, 3 MAY 2001.
[57]汪小帆,李翔,陈关荣编著.复杂网络——理论及其应用.北京:清华大学出版社.2006.4.
[58] Granovetter M. The Strength of Weak Ties. American Journal of Sociology. 1973,78(6):1360~1380.
[59] Flache A and Macy MW. The Weakness of Strong Ties: Collective Action Failure in a Highly Cohesive Group. Journal of Mathematical Sociology, June, 1996.
[60] Michael W. Macy , James Kitts, and Andreas Flache. The Weakness of Strong Ties II: Collective Action Failure in a Self-Organizing Social Network. American Sociological Association, Toronto,August 11, 1997
[61] Coleman, James S, Elihu Katz, and Herbert Menzel. 1966. Medical Innovation: A Diffusion Study Indianapolis, IN: Bobbs-Merrill.
[62] Granovetter, M. 1978.“Threshold Models of Collective Behavior.”American Journal of Sociology 83:1420-1443.
[63] Damon Centola and Michael W. Macy. Complex Contagion and the Weakness of Long Ties Revise and Resubmit, American Journal of Sociology
[64] M. E. J. Newman, D. J. Watts. Renormalization group analysis of the small-world network model. Phys Lett A, 1999, 263: 341-346
[65] Axelrod, R. 1997. The Dissemination of Culture: A Model with Local Convergence and Global Polarization. Journal of Conflict Resolution 41:203-226.
[66] http://www.swarm.org/wiki/Main_Page
[67] http://repast.sourceforge.net/
[68] http://ccl.northwestern.edu/netlogo/
[2]魏宏森,宋永华等.开创复杂性研究的新学科——系统科学纵览.出版社:四川教育出版社. 1991年12月第1版.
[3]贝塔朗菲.一般系统论——基础,发展,应用.北京:社会科学文献出版社. 1987.
[4]维纳N.控制论.郝季仁译.北京:科学出版社. 1963.
[5]香农E.通信的数学理论.沈永朝译.北京:求实出版社. 1989. 508-600.
[6]尼克利斯G,普利高津I.非平衡系统的自组织.徐锡申等译.北京:科学出版社,1986.
[7]哈肯H.协同学引论.徐锡申等译.北京:原子能出版社. 1984.
[8]艾根M,舒斯特P.曾国屏、沈小峰译.超循环论.上海:上海译文出版社,1990.
[9] Neumann JV. Theory of Self-reproducing Automata. University of Illinois Press. 1966
[10]李建会,张江.数字创世纪:人工生命的新科学.北京:科学出版社.2005.12.
[11] S. Wolfram. Cellular Automata as Simple Self-Organizing Systems. Caltech preprint CALT-68-938, 1982.
[12]袁崇义. PETRI网原理.北京:电子工业出版社. 1998.4.
[13] Forrester JW. Industrial Dynamics. Cambridge: MIT Press, 1961.
[14] http://jasss.soc.surrey.ac.uk/JASSS.html
[15] Dianne CB. ASPEN-EE: An Agent-Based Model of Infrastructure Interdependency. Sandia Report 2000.
[16] Epstein JM, Axtell R. Growing Artificial Societies: Social Science from the Bottom up. Washington, D.C.: Brookings Institution Press. 1996.
[17]张江,基于Agent的计算经济学建模方法及其关键技术研究[D(]博士学位论文)2005
[18] Shi YR, Zhang J, Gao L and Zhou C. Scale-Free Networks Emerge out of Micro-Mechanism in an Agent-based Computational Economic Model
[19]约翰·霍兰著.周晓牧,韩晖译.隐秩序-适应性造就复杂性.上海科技教育出版社,2001.
[20] http://www.red3d.com/cwr/boids/
[21] Axelrod R. The Evolution of Cooperation. New York: Basic Books, 1984.
[22] Arthur B, et al. Asset Pricing Under Endogenous Expectations. Santa Fe Institute Paper, 1996.
[23]霍兰,陈禹等译.涌现--从混沌到秩序.上海:上海科学技术出版社. 2001.
[24]张江.基于Agent的计算经济学建模方法及其关键技术研究博士学位论文,北京交通大学.
[25]方美琪,张树人编著.复杂系统建模与仿真.北京:人民大学出版社. 2005.
[26] Howitt P, Clower R. The emergence of economic organization. Journal of Economic Behavior & Organization. Vol. 41. (2000): 55-84.
[27] Wilhite A. Bilateral Trade and‘Small-World’Networks. Computational Economics Vol. 18.(2001): 49–64.
[28] Pujol JM, Flache A, Delgado J and Sangüesa J, How Can Social Networks Ever Become Complex? Modelling the Emergence of Complex Networks from Local Social Exchanges. Journal of Artificial Societies and Social Simulation. vol. 8, no. 4 ( 2005 ) . http://jasss.soc.surrey.ac.uk/8/4/12.html
[29] Tesfatsion L. Agent-Based Computational Economics. ISU Economics Working Paper No. 1, Revised August 24, 2003.
[30] Schelling TC. Micromotives and Macrobehavior. W. W. Norton & Company, 1978.
[31] Kiyotaki N, Wright R. On money as a medium of exchange. Journal of Political Economy, 1989, vol 0(97): 927~954.
[32] Lane D: Artificial worlds and economics. Journal of Evolutionary Economics. 1992. vol 0(3): 89~107: 89~107.
[33] http://www.econ.iastate.edu/tesfatsi/ace.htm
[34] Gintis, H. Game theory evolving. Princeton, NJ: The Princeton University Press. 2000.
[35] Rust, J., Miller, J. H., and Palmer, R. Characterizing effective trading strategies: Insights from a computerized double auction tournament. Journal of Economic Dynamics and Control 1994. 18, 61–96.
[36] Gode, DK and Sunder, S. Allocative efficiency of markets with zero-intelligence traders: Market as a partial substitute for individual rationality [J]. Journal of Political Economy 1996. 101, 119–137.
[37] Vriend, NJ. Self-organization of markets: An example of a computational approach[J]. Computational Economics 1995. 8: 205–231.
[38] Edmonds B, Moss S. From KISS to KIDS-an "anti-simplistic" modeling approach. Davidsson Paul, Logan Brian et.al: Multi-Agent and Multi-Agent-Based Simulation: Joint Workshop MABS 2004 (Lecture Notes in Computer Science / Lecture Notes in Artificial Intelligence), Springer: 2005. 130-144
[39] Claudia PW, Ebenoth E. An Adaptive Toolbox Model: a pluralistic modelling approach for human behaviour based on observation. Journal of Artificial Societies and Social Simulation, vol. 7(1)http://jasss.soc.surrey.ac.uk/7/1/3.html
[40] Sun R. and Naveh I.Simulating Organizational Decision-Making Using a Cognitively Realistic Agent Model [J]. Journal of Artificial Societies and Social Simulation, 2004. vol. 7(3)http://jasss.soc.surrey.ac.uk/7/3/5.html
[41] Prietula, M. J., Carley, K. M., and Gasser, L. Simulating organizations: Computational models of institutions and groups [M]. Cambridge, MA: The MIT Press.
[42] Dawid, H, Reimann, M., and Bullnheimer, B. To innovate or not to innovate? IEEE Transactions on Evolutionary Computation 2001. 5: 471–481.
[43]张江,李学伟.用数字人工生命模型探索复杂适应系统,复杂系统与复杂性科学第2卷第1期2005年1月.
[44] Holland J, Genetic algorithms and Classifier Systems: Foundations and Future Directions. in Proceedings of the Second International Conference on Genetic Algorithms, Lawrence Erlbaum Associates, publishers, 1987, pp. 82-89.
[45]卢代富.国外企业社会责任界说评述.现代法学,2001 (6): 137-144.
[46]斯蒂芬p.罗宾斯管理学〔第四版〕.北京.中国人民大学出版社:1997年4月.
[47] Carroll, A. B. Corporate Social Responsibility: Evolution of a Definitional Construct [J]. Business and Society, 1999, 38(3): 268-295.
[48] Varleri Paone. Challenging Corporate Social Responsibility: The Emerging Factor. The fifth Asian Academy of Management Conference & AOM. Tokyo December 2006.
[49]陆征一周义仓.数学生物进展.科学出版社出版. 2006.4.
[50] Solomon S. Generalized Lotka-Volterra (GLV) Models and Generic Emergence of Scaling Laws in Stock Markets. in "Applications of Simulation to Social Sciences" ,Eds: G Ballot and G Weisbuch; Hermes Science Publications 2000.
[51] Faust,K.1994.Social Networks Analysis: Methods and Applications. Cambridge, England: Cambridge University Press.
[52] Watts J S, Strogatz S H. Collective dynamics of‘small-world’networks. Nature, 1998, 393: 440.
[53] Faloutsos M, Faloutsos P, Faloutsos C. On power-law relationships of the Internet topology. Computer Communications Review, 1999, 29: 251
[54] Sen P et al. Small-world properties of the Indian railway network. Phys. Rev. E, 2003, 67: 036106.
[55] Barabasi AL, Albert R. Emergence of scaling in random networks. Science, 1999, 286(5439):509~512.
[56] Jeong H, Mason SP, Barabási AL, Oltvai ZN. Lethality and centrality in protein networks NATURE. VOL 411, 3 MAY 2001.
[57]汪小帆,李翔,陈关荣编著.复杂网络——理论及其应用.北京:清华大学出版社.2006.4.
[58] Granovetter M. The Strength of Weak Ties. American Journal of Sociology. 1973,78(6):1360~1380.
[59] Flache A and Macy MW. The Weakness of Strong Ties: Collective Action Failure in a Highly Cohesive Group. Journal of Mathematical Sociology, June, 1996.
[60] Michael W. Macy , James Kitts, and Andreas Flache. The Weakness of Strong Ties II: Collective Action Failure in a Self-Organizing Social Network. American Sociological Association, Toronto,August 11, 1997
[61] Coleman, James S, Elihu Katz, and Herbert Menzel. 1966. Medical Innovation: A Diffusion Study Indianapolis, IN: Bobbs-Merrill.
[62] Granovetter, M. 1978.“Threshold Models of Collective Behavior.”American Journal of Sociology 83:1420-1443.
[63] Damon Centola and Michael W. Macy. Complex Contagion and the Weakness of Long Ties Revise and Resubmit, American Journal of Sociology
[64] M. E. J. Newman, D. J. Watts. Renormalization group analysis of the small-world network model. Phys Lett A, 1999, 263: 341-346
[65] Axelrod, R. 1997. The Dissemination of Culture: A Model with Local Convergence and Global Polarization. Journal of Conflict Resolution 41:203-226.
[66] http://www.swarm.org/wiki/Main_Page
[67] http://repast.sourceforge.net/
[68] http://ccl.northwestern.edu/netlogo/