基于熵和集对分析理论的复杂系统的脆性研究
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摘要
在本论文中,首先通过介绍复杂系统研究的现阶段发展情况,说明了研究复杂系统脆性的重要性。接着在介绍复杂系统的同时,给出了本文对复杂系统的定义及判断方法。
其次,在对复杂系统的研究的基础之上,首次提出脆性是复杂系统的一个基本特性。给出了系统的脆性的定义,脆性的特点,以及脆性基元的结构,为复杂系统的脆性的进一步分析建立了理论基础。接着, 在一个脆性基元内,定义了子系统脆性同一、对立、波动,以及脆性联系函数的概念。进而,利用集对分析理论,定义了系统脆性联系熵的概念。
进一步,在复杂系统脆性理论的研究中引入非合作博弈的理论,指出正是由于各个子系统为了追求个体利益,而导致了整个复杂系统的整体利益的损失。环境的负熵并非取之不尽,非合作争取负熵的结果导致了系统的脆性激发而崩溃。
最后,在非合作博弈状况下对复杂系统脆性进行模拟仿真,仿真结果说明,非合作博弈和系统的脆性熵增是导致系统崩溃的原因,但是通过有效的手段可以使系统免于崩溃。
In this paper, according to the development of the present stage on research of complex system importance of research of complex system’s brittleness is pointed out. In the process of introducing complex system, we give the concept of complex system and method of judgement.
Secondly, Based on the research of complex system, brittleness as one of the basic characteristics has been presented and argued for the first time. We give the definition of the brittleness, the characteristic of the brittleness, and the structure of the brittle basic element, for further analysis of complex system’s brittleness laid the theoretical foundation. And, brittle sameness, brittle opposite, brittle fluctuation and brittle link function is established in a brittle basic element. Meanwhile, according to set pair theory, concepts of brittle link entropy is defined.
Moreover, non-cooperative game theory is applied to meet the need of the research on the brittleness of complex system, just because the different subsystems pursue individual profit, the whole interest of complex system has to see the loss. When the subsystems cannot obtain the negative entropy from the environment, the entropy will reach the critical point of collapse.
Finally, under the environment of non-cooperative game dynamics, the brittle simulation model has been established. The results of simulation show that the collapse of complex is due to the entropy increase of subsystems in a brittle basic element and non-cooperative game dynamics, however, the effective means can make the system avoid collapsing.
其次,在对复杂系统的研究的基础之上,首次提出脆性是复杂系统的一个基本特性。给出了系统的脆性的定义,脆性的特点,以及脆性基元的结构,为复杂系统的脆性的进一步分析建立了理论基础。接着, 在一个脆性基元内,定义了子系统脆性同一、对立、波动,以及脆性联系函数的概念。进而,利用集对分析理论,定义了系统脆性联系熵的概念。
进一步,在复杂系统脆性理论的研究中引入非合作博弈的理论,指出正是由于各个子系统为了追求个体利益,而导致了整个复杂系统的整体利益的损失。环境的负熵并非取之不尽,非合作争取负熵的结果导致了系统的脆性激发而崩溃。
最后,在非合作博弈状况下对复杂系统脆性进行模拟仿真,仿真结果说明,非合作博弈和系统的脆性熵增是导致系统崩溃的原因,但是通过有效的手段可以使系统免于崩溃。
In this paper, according to the development of the present stage on research of complex system importance of research of complex system’s brittleness is pointed out. In the process of introducing complex system, we give the concept of complex system and method of judgement.
Secondly, Based on the research of complex system, brittleness as one of the basic characteristics has been presented and argued for the first time. We give the definition of the brittleness, the characteristic of the brittleness, and the structure of the brittle basic element, for further analysis of complex system’s brittleness laid the theoretical foundation. And, brittle sameness, brittle opposite, brittle fluctuation and brittle link function is established in a brittle basic element. Meanwhile, according to set pair theory, concepts of brittle link entropy is defined.
Moreover, non-cooperative game theory is applied to meet the need of the research on the brittleness of complex system, just because the different subsystems pursue individual profit, the whole interest of complex system has to see the loss. When the subsystems cannot obtain the negative entropy from the environment, the entropy will reach the critical point of collapse.
Finally, under the environment of non-cooperative game dynamics, the brittle simulation model has been established. The results of simulation show that the collapse of complex is due to the entropy increase of subsystems in a brittle basic element and non-cooperative game dynamics, however, the effective means can make the system avoid collapsing.
引文
1 Bertalanffy L V. General System Theory [M]. New York, 1968
2 尼科里斯,普里高津.探索复杂性.罗久里,陈奎宁译.成都:四川教育出版社,1986:1～23
3 哈肯.高等协同学.郭治安译.北京:科学出版社,1989:1～20
4 Auyang, S.Y. Foundations of Complex-System Theories in Economics, Evolutionary Biology, and Statistical Physics. Cambridge University Press, New York, 1998:404
5 钱学森,于景元,戴汝为.一个科学的新领域——开放的复杂巨系统及其方法论. 自然杂志. 1990,13(3): 3～10
6 苗东升.复杂性研究的现状与展望.系统辩证学学报.2001,9(4): 3～9
7 颜泽贤,陈忠,胡皓编.复杂系统演化论.人民出版社,1993 年12 月:40～70
8 姜璐.复杂系统的层次结构.自然辩证法研究.1994 年,第10 卷第2 期:16～21
9 李夏, 戴汝为.系统科学与复杂性.自动化学报.1998 年3 月,第24 卷第2期:200～207
10 Ang, A.H.S.Pires, J.A. A Model for The Seismic Reliability Assessment of Electric Power Transmission Systems. Reliability Engineering &system safety.1996, 51(1): 7～22
11 Rennaker, P.R.Richardson. New Approach to Vulnerability Assessment. Journal of the American Helicopter Society. 1999, 44(1): 38～41
12 Soutter, Marc Musy, Andre. Global Sensitivity Analyses of Three Pesticide Leaching Models Using a Monte-Carlo Approach. Journal of Environmental Quality.1999, 28(4): 1290～1297
13 Soutter, Marc Musy, Andre. Coupling 1D Monte-Carlo Simulations and Geostatistics to Assess Groundwater Vulnerability to Pesticide Contamination on A regional scale. Journal of Contaminant Hydrology. 1998, 32(1-2): 25～29
14 王经民,王有科. 黄土高原生态环境脆弱性计算方法探讨. 水土保持通报.1996(32): 36～43
15 Monton, V.Ward. Risk Assessment Methodology for Network Integrity. BT Technology Journal. 1997,15(10): 223～234
16 E.Akiyamaa, K.Kanekob. Dynamical Systems Game Theory and Dynamics of Games. Physic D, 2000(147): 221～258
17 Lind, Niels C. Measure of Vulnerability and Damage Tolerance. Reliability Engineering & System Safety.1995, 48(1): 1～6
18 任鲁川.灾害熵:概念引入及应用案例.自然灾害学报.2000,9(2): 26～31
19 Zbigniew Szwast, Stanislaw Sieniutycz, J.S.Shiner. Complexity Principle of Extremality in Evolution of Living Organism by Information-theoretic Entropy. Chaos, Solitons and Fractals. 2002,13:1871～1888
20 M.X. He, P.E. Ricci. Information Entropy of Orthogonal Polynomials. Applied Mathematics and Computation .2002,128: 261～274
21 Giuseppe Ricciardia, Isaac Elishako. A Novel Local Stochastic Linearization Method Via Two extremum Entropy Principles. International Journal of Non-Linear Mechanics. 2002,37: 785～800
22 林康镛.关于熵概念的扩充问题.青岛建筑工程学院学报.1992,13(1):73～77
23 任叔良, 赵克勤. 集对分析在企业能源管理中的应用探讨. 能源工程.1996,(3 ) :21～2 3
24 朱其秀.关于联系数的同异反态势熵及应用.绍兴文理学院学报. 2000,20(6):87～89
25 赵克勤,宣爱理.集对论——一种新的不确定性理论、方法、应用.系统工程,1 996,(1):1 8～2 3
26 王霞,彭晓华.集对分析中差异度系数i 的取值方法及应用.天津轻工业学院学报.2002,4:56～58
27 Jae C. Oh. Promoting Cooperation Using ‘kin’Biased Conditional Strategy in The Iterated Prisoner’s Dilemma Game. Information Science. 2001,133:149～164
28 Paul A. Samuelson. Some Game Theory Anecdotes. Japan and the World Economy.2001, 13: 299～302
29 Eizo Akiyamaa, Kunihiko Kaneko. Dynamical Systems Game Theory II. A New Approach to The Problem of The Social Dilemma. Physic D. 2002, 2891:1～36
30 叶民强,林峰.区域人口、资源与环境公平性问题的博弈分析.上海财经大学学报. 2001,3(5):10～15
31 John Nash,贝兴亚译.非合作博弈.系统工程.1996,14(2):21～26
32 http://www.moh.gov.cn
33 Vassalos, Dracos, Turan, Osman, Pawlowski, Maciej. Dynamic Stability Assessment of Damaged Passenger/ro-ro Ships and Proposal of Rational Survival Criteria. Marine Technology. 1997,34(4): 241～266
34 邢修三. 物理熵、信息熵及其演化方程.中国科学(A 辑).2001,31(1):77～84
35 A.G. Bashkirov, A.V. Vityazev. Information Entropy and Power-law Distributions for Chaotic Systems. Physica A. 2000 (277): 136-145
36 张斌. 不确定信息处理的集对论思想方法[J]. 模糊系统与数学. 2001,15(2): 89～93
37 Michele Damicoa, Giovanni Manzinib,Luciano Margarac. On Computing The Entropy of Cellular Automata. Theoretical Computer Science. 2003 (290): 1629～1646
38 Anthony N.Kounadis. Dynamic Buckling of Simple Two-bar Frames Using Catastrophe Theory. International Journal of Non-Linear Mechanics. 2002(37): 1249～1259
39 Marco Carricato, Joseph Du.y, Vincenzo Parenti-Castelli. Catastrophe Analysis of A Planar System with Flexural Pivots. Mechanism and Machine. 2002(37):693～716
40 WEI Qi, JIN Hongzhang, JI Ming. The Research on Brittle Catastrophe of Complex Giant System. IEEE Region 10 Technical Conference on Computers, Communications, Control and Power Engineering (TENCON’02) October 28-31, 2002 Beijing, CHINA
41 董国兴. 运用熵原理探讨环境污染与环境保护.职大学报.2004,(2):1～4
42 邢修三. 论动态统计信息理论. 北京理工大学学报. 2004, 24(1):1～15
43 黄沛天,胡利云. 对负熵、信息熵和熵原理等概念之厘清. 现代物理知识.2004, (3):21～23
44 张连明,陈志刚,邓晓衡. 一种基于信息熵的Internet 宏观行为模型研究. 2004,(19):33～37
45 葛永林. 生命自组织进化的实质. 系统辩证学学报.2004,12(4):79～82
46 WEI Qi, JIN Hongzhang, GUO Jian, JI Ming. Analysis on The Collapse of Complex System Based on The Brittle Characteristic. 2002 International Symposium on Nonlinear Theory and its Applications (NOLTA 2002)
47 孙晋众,陈世权. 一种集对分析的动态模型极其应用. 系统工程. 2004, 22(5):35～38
2 尼科里斯,普里高津.探索复杂性.罗久里,陈奎宁译.成都:四川教育出版社,1986:1～23
3 哈肯.高等协同学.郭治安译.北京:科学出版社,1989:1～20
4 Auyang, S.Y. Foundations of Complex-System Theories in Economics, Evolutionary Biology, and Statistical Physics. Cambridge University Press, New York, 1998:404
5 钱学森,于景元,戴汝为.一个科学的新领域——开放的复杂巨系统及其方法论. 自然杂志. 1990,13(3): 3～10
6 苗东升.复杂性研究的现状与展望.系统辩证学学报.2001,9(4): 3～9
7 颜泽贤,陈忠,胡皓编.复杂系统演化论.人民出版社,1993 年12 月:40～70
8 姜璐.复杂系统的层次结构.自然辩证法研究.1994 年,第10 卷第2 期:16～21
9 李夏, 戴汝为.系统科学与复杂性.自动化学报.1998 年3 月,第24 卷第2期:200～207
10 Ang, A.H.S.Pires, J.A. A Model for The Seismic Reliability Assessment of Electric Power Transmission Systems. Reliability Engineering &system safety.1996, 51(1): 7～22
11 Rennaker, P.R.Richardson. New Approach to Vulnerability Assessment. Journal of the American Helicopter Society. 1999, 44(1): 38～41
12 Soutter, Marc Musy, Andre. Global Sensitivity Analyses of Three Pesticide Leaching Models Using a Monte-Carlo Approach. Journal of Environmental Quality.1999, 28(4): 1290～1297
13 Soutter, Marc Musy, Andre. Coupling 1D Monte-Carlo Simulations and Geostatistics to Assess Groundwater Vulnerability to Pesticide Contamination on A regional scale. Journal of Contaminant Hydrology. 1998, 32(1-2): 25～29
14 王经民,王有科. 黄土高原生态环境脆弱性计算方法探讨. 水土保持通报.1996(32): 36～43
15 Monton, V.Ward. Risk Assessment Methodology for Network Integrity. BT Technology Journal. 1997,15(10): 223～234
16 E.Akiyamaa, K.Kanekob. Dynamical Systems Game Theory and Dynamics of Games. Physic D, 2000(147): 221～258
17 Lind, Niels C. Measure of Vulnerability and Damage Tolerance. Reliability Engineering & System Safety.1995, 48(1): 1～6
18 任鲁川.灾害熵:概念引入及应用案例.自然灾害学报.2000,9(2): 26～31
19 Zbigniew Szwast, Stanislaw Sieniutycz, J.S.Shiner. Complexity Principle of Extremality in Evolution of Living Organism by Information-theoretic Entropy. Chaos, Solitons and Fractals. 2002,13:1871～1888
20 M.X. He, P.E. Ricci. Information Entropy of Orthogonal Polynomials. Applied Mathematics and Computation .2002,128: 261～274
21 Giuseppe Ricciardia, Isaac Elishako. A Novel Local Stochastic Linearization Method Via Two extremum Entropy Principles. International Journal of Non-Linear Mechanics. 2002,37: 785～800
22 林康镛.关于熵概念的扩充问题.青岛建筑工程学院学报.1992,13(1):73～77
23 任叔良, 赵克勤. 集对分析在企业能源管理中的应用探讨. 能源工程.1996,(3 ) :21～2 3
24 朱其秀.关于联系数的同异反态势熵及应用.绍兴文理学院学报. 2000,20(6):87～89
25 赵克勤,宣爱理.集对论——一种新的不确定性理论、方法、应用.系统工程,1 996,(1):1 8～2 3
26 王霞,彭晓华.集对分析中差异度系数i 的取值方法及应用.天津轻工业学院学报.2002,4:56～58
27 Jae C. Oh. Promoting Cooperation Using ‘kin’Biased Conditional Strategy in The Iterated Prisoner’s Dilemma Game. Information Science. 2001,133:149～164
28 Paul A. Samuelson. Some Game Theory Anecdotes. Japan and the World Economy.2001, 13: 299～302
29 Eizo Akiyamaa, Kunihiko Kaneko. Dynamical Systems Game Theory II. A New Approach to The Problem of The Social Dilemma. Physic D. 2002, 2891:1～36
30 叶民强,林峰.区域人口、资源与环境公平性问题的博弈分析.上海财经大学学报. 2001,3(5):10～15
31 John Nash,贝兴亚译.非合作博弈.系统工程.1996,14(2):21～26
32 http://www.moh.gov.cn
33 Vassalos, Dracos, Turan, Osman, Pawlowski, Maciej. Dynamic Stability Assessment of Damaged Passenger/ro-ro Ships and Proposal of Rational Survival Criteria. Marine Technology. 1997,34(4): 241～266
34 邢修三. 物理熵、信息熵及其演化方程.中国科学(A 辑).2001,31(1):77～84
35 A.G. Bashkirov, A.V. Vityazev. Information Entropy and Power-law Distributions for Chaotic Systems. Physica A. 2000 (277): 136-145
36 张斌. 不确定信息处理的集对论思想方法[J]. 模糊系统与数学. 2001,15(2): 89～93
37 Michele Damicoa, Giovanni Manzinib,Luciano Margarac. On Computing The Entropy of Cellular Automata. Theoretical Computer Science. 2003 (290): 1629～1646
38 Anthony N.Kounadis. Dynamic Buckling of Simple Two-bar Frames Using Catastrophe Theory. International Journal of Non-Linear Mechanics. 2002(37): 1249～1259
39 Marco Carricato, Joseph Du.y, Vincenzo Parenti-Castelli. Catastrophe Analysis of A Planar System with Flexural Pivots. Mechanism and Machine. 2002(37):693～716
40 WEI Qi, JIN Hongzhang, JI Ming. The Research on Brittle Catastrophe of Complex Giant System. IEEE Region 10 Technical Conference on Computers, Communications, Control and Power Engineering (TENCON’02) October 28-31, 2002 Beijing, CHINA
41 董国兴. 运用熵原理探讨环境污染与环境保护.职大学报.2004,(2):1～4
42 邢修三. 论动态统计信息理论. 北京理工大学学报. 2004, 24(1):1～15
43 黄沛天,胡利云. 对负熵、信息熵和熵原理等概念之厘清. 现代物理知识.2004, (3):21～23
44 张连明,陈志刚,邓晓衡. 一种基于信息熵的Internet 宏观行为模型研究. 2004,(19):33～37
45 葛永林. 生命自组织进化的实质. 系统辩证学学报.2004,12(4):79～82
46 WEI Qi, JIN Hongzhang, GUO Jian, JI Ming. Analysis on The Collapse of Complex System Based on The Brittle Characteristic. 2002 International Symposium on Nonlinear Theory and its Applications (NOLTA 2002)
47 孙晋众,陈世权. 一种集对分析的动态模型极其应用. 系统工程. 2004, 22(5):35～38