复杂系统脆性理论及其在危机分析中的应用
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摘要
随着社会经济、科学技术的发展，人们为了追求舒适的生活，导致各个与国计民生相关的复杂系统的规模越来越大。一旦复杂系统中的一个子系统在内外干扰下发生崩溃而不能正常的工作，整个复杂系统便会可能失去了它应有的功能，而出现整体坍塌。
本论文以复杂系统作为研究对象，首次提出脆性是复杂系统的一个基本特性，即复杂系统除了具有开放性、复杂性、巨量性、进化与涌现性、层次性之外，还具有脆性。而且指出脆性作为复杂系统的一个基本特性是客观存在的。在给出脆性的定义、特点和模型的基础之上，建立了复杂系统脆性的相关概念、理论。并将此理论用于分析和处理非典型性肺炎给复杂系统带来的影响和危机。
首先，针对复杂系统脆性的定义和特点进行研究。从材料力学领域关于脆性的定义出发，将其引申到复杂系统特性的研究中。复杂系统脆性重点强调崩溃的连锁效应，即由于复杂系统中的某一子系统的崩溃，引发的连锁的崩溃效应，会使整个复杂系统崩溃。以脆性定义为基础，分析了复杂系统脆性的基本特点。脆性具有以下的特点：隐藏性、伴随性、作用结果的表现形式的多样性、作用结果危害的严重性、子系统之间的非合作博弈关系是复杂系统脆性的一个根源、连锁性、延时性、整合性。
其次，为了形象化说明复杂系统脆性的概念，提出了多米诺骨牌模型、金字塔与倒金字塔模型、元胞自动机模型等几种基本模型。同时，为了分析各个子系统间的脆性联系，以脆性联系函数为基础建立了脆性同一度、对立度、波动度、脆性变化率和子系统的脆性相关序列等一系列的相关的概念，定性地分析了各个子系统之间的脆性联系。
再次，建立了复杂系统脆性研究的理论基础。根据集对分析的理论和方法，在复杂系统的一个脆性基元内，建立了脆性联系熵的概念。即当一个脆性基元内的子系统崩溃后，其它子系统功能与状态，受崩溃的子系统所影响的程度，体现在脆性同一熵、对立熵、波动熵三个方面。在崩溃的子系统的影响下，未崩溃的子系统为了自己的生存，需要从外界环境获得负熵流，来降低而由于脆性联系熵导致它们的熵增，且它们之间的关系属于非合作博弈。若外界环境的负熵流无法满足时，它们的脆性熵将达到使它们发生崩溃的临
哈尔滨工程大学博士学位论文
界值。利用元胞自动机模拟整个复杂系统的脆性，将每一个子系统作为一个
元胞，建立以Von.Neumann型为基础的复杂系统的元胞自动机脆性仿真规
则。以突变级数法为基础，在一个脆性基元内，利用尖点突变级数法和燕尾
突变级数法进行脆性评价。当一个子系统在干扰下崩溃后，根据尚未崩溃的
子系统与崩溃的子系统之间的同一度、对立度、波动度来评价它们之间的脆
性关系。
最后，将复杂系统脆性理论应用于非典型性肺炎危机的脆性研究。根据
国家卫生部2003年4月下旬到5月上旬期间发布的非典型性肺炎疫情通报，
以北京、内蒙古为例，从复杂系统脆性的角度来分析非典型性肺炎危机，提
出相应的危机处理策略。
With the development of social economy and science and technology, the scale of various complex systems related to the national economy and the people's livelihood becomes larger and larger because people want to pursue more comfortable life. Consequently, after one subsystem of complex system cannot be in good operation under the interferences from inside and outside, it is possible for the whole complex system to lose its functions and to be collapsed.
In this paper, complex system is chosen as the research object, which is characterized not only by openness, complexity, giant, evolution and emergence, hierarchy but also by brittleness. Brittleness is presented as one of the basic characteristics of complex system for the first time. Moreover, it is existent objectively as the basic characteristic of complex system. Based on the definition, peculiarities, and models of brittleness, concepts and theories about brittleness of complex system have been established, which is applied for analyzing the effect and crisis brought by the severe acute respiratory syndrome.
Firstly, research has been carried out on the definition and peculiarities of brittleness. Brittleness comes from the term in the field of material science, which is defined and applied to the research on the characteristics of the complex system. Brittleness emphasizes on the collapsed chain effect that is triggered by the collapse of one subsystem and will result in the breakdown of whole complex system. On the basis of its definition, peculiarities of brittleness have been analyzed. They are recessive, concomitance, diverse representations of results, catastrophic and serious results, non-cooperative game between subsystems being one source of brittleness, chain effect, delay effect, represented from the angle of whole system.
Secondly, domino model, pyramid model, reverse pyramid model, and cellular automaton model have been presented in order to explain the concepts of brittleness clearly. Meanwhile, based on the brittle link function, a series of concepts are defined such as same degree, opposite degree, fluctuating degree, brittleness varying ratio, brittleness correlated series between subsystems, which analyzes the brittle link between the subsystems qualitatively.
Thirdly, theoretical basis of complex system brittleness has been set up. The concept of brittle link entropy is established according to the theory of set pairing in a brittle basic element. That is to say after a subsystem is collapsed, the states and functions of other ones will be affected in three aspects including brittle
sameness entropy, brittle opposite entropy, brittle fluctuation entropy. Certainly, influenced by the collapsed subsystem, the non-collapsed ones compete with each other for their own survival by the means of non-cooperative game. They have to gain negative entropy from the environment so that they can reduce the increase of entropy from the brittle link entropy of the collapsed subsystem. If they cannot be satisfied, their entropy will increase to the critical point that results in their collapse. In order to simulate the brittle behavior of complex system, theory of cellular automaton has been induced to describe the macro reflection of brittleness in one/complex system. Von. Neumann model is applied, which a subsystem is regarded as one cellular. The simulation rules have also been established. In a brittle basic element, brittle evaluations have been finished by employing cusp and swallow catastrophe progression methods, which brittle relation between the non-collapsed subsystems and the collapsed one ca
n be evaluated according to the brittle same degree, brittle opposite degree and brittle fluctuating degree.
Finally, on the basis of data from the Ministry of Health P.R.China from April to May, taking Beijing, and Nei Menggu as examples, brittleness research and analyses have been carried out on the S ARS based on the theory of brittleness. Then, effective methods are presented from the point of view of brittleness in order to deal with the crisis.
本论文以复杂系统作为研究对象，首次提出脆性是复杂系统的一个基本特性，即复杂系统除了具有开放性、复杂性、巨量性、进化与涌现性、层次性之外，还具有脆性。而且指出脆性作为复杂系统的一个基本特性是客观存在的。在给出脆性的定义、特点和模型的基础之上，建立了复杂系统脆性的相关概念、理论。并将此理论用于分析和处理非典型性肺炎给复杂系统带来的影响和危机。
首先，针对复杂系统脆性的定义和特点进行研究。从材料力学领域关于脆性的定义出发，将其引申到复杂系统特性的研究中。复杂系统脆性重点强调崩溃的连锁效应，即由于复杂系统中的某一子系统的崩溃，引发的连锁的崩溃效应，会使整个复杂系统崩溃。以脆性定义为基础，分析了复杂系统脆性的基本特点。脆性具有以下的特点：隐藏性、伴随性、作用结果的表现形式的多样性、作用结果危害的严重性、子系统之间的非合作博弈关系是复杂系统脆性的一个根源、连锁性、延时性、整合性。
其次，为了形象化说明复杂系统脆性的概念，提出了多米诺骨牌模型、金字塔与倒金字塔模型、元胞自动机模型等几种基本模型。同时，为了分析各个子系统间的脆性联系，以脆性联系函数为基础建立了脆性同一度、对立度、波动度、脆性变化率和子系统的脆性相关序列等一系列的相关的概念，定性地分析了各个子系统之间的脆性联系。
再次，建立了复杂系统脆性研究的理论基础。根据集对分析的理论和方法，在复杂系统的一个脆性基元内，建立了脆性联系熵的概念。即当一个脆性基元内的子系统崩溃后，其它子系统功能与状态，受崩溃的子系统所影响的程度，体现在脆性同一熵、对立熵、波动熵三个方面。在崩溃的子系统的影响下，未崩溃的子系统为了自己的生存，需要从外界环境获得负熵流，来降低而由于脆性联系熵导致它们的熵增，且它们之间的关系属于非合作博弈。若外界环境的负熵流无法满足时，它们的脆性熵将达到使它们发生崩溃的临
哈尔滨工程大学博士学位论文
界值。利用元胞自动机模拟整个复杂系统的脆性，将每一个子系统作为一个
元胞，建立以Von.Neumann型为基础的复杂系统的元胞自动机脆性仿真规
则。以突变级数法为基础，在一个脆性基元内，利用尖点突变级数法和燕尾
突变级数法进行脆性评价。当一个子系统在干扰下崩溃后，根据尚未崩溃的
子系统与崩溃的子系统之间的同一度、对立度、波动度来评价它们之间的脆
性关系。
最后，将复杂系统脆性理论应用于非典型性肺炎危机的脆性研究。根据
国家卫生部2003年4月下旬到5月上旬期间发布的非典型性肺炎疫情通报，
以北京、内蒙古为例，从复杂系统脆性的角度来分析非典型性肺炎危机，提
出相应的危机处理策略。
With the development of social economy and science and technology, the scale of various complex systems related to the national economy and the people's livelihood becomes larger and larger because people want to pursue more comfortable life. Consequently, after one subsystem of complex system cannot be in good operation under the interferences from inside and outside, it is possible for the whole complex system to lose its functions and to be collapsed.
In this paper, complex system is chosen as the research object, which is characterized not only by openness, complexity, giant, evolution and emergence, hierarchy but also by brittleness. Brittleness is presented as one of the basic characteristics of complex system for the first time. Moreover, it is existent objectively as the basic characteristic of complex system. Based on the definition, peculiarities, and models of brittleness, concepts and theories about brittleness of complex system have been established, which is applied for analyzing the effect and crisis brought by the severe acute respiratory syndrome.
Firstly, research has been carried out on the definition and peculiarities of brittleness. Brittleness comes from the term in the field of material science, which is defined and applied to the research on the characteristics of the complex system. Brittleness emphasizes on the collapsed chain effect that is triggered by the collapse of one subsystem and will result in the breakdown of whole complex system. On the basis of its definition, peculiarities of brittleness have been analyzed. They are recessive, concomitance, diverse representations of results, catastrophic and serious results, non-cooperative game between subsystems being one source of brittleness, chain effect, delay effect, represented from the angle of whole system.
Secondly, domino model, pyramid model, reverse pyramid model, and cellular automaton model have been presented in order to explain the concepts of brittleness clearly. Meanwhile, based on the brittle link function, a series of concepts are defined such as same degree, opposite degree, fluctuating degree, brittleness varying ratio, brittleness correlated series between subsystems, which analyzes the brittle link between the subsystems qualitatively.
Thirdly, theoretical basis of complex system brittleness has been set up. The concept of brittle link entropy is established according to the theory of set pairing in a brittle basic element. That is to say after a subsystem is collapsed, the states and functions of other ones will be affected in three aspects including brittle
sameness entropy, brittle opposite entropy, brittle fluctuation entropy. Certainly, influenced by the collapsed subsystem, the non-collapsed ones compete with each other for their own survival by the means of non-cooperative game. They have to gain negative entropy from the environment so that they can reduce the increase of entropy from the brittle link entropy of the collapsed subsystem. If they cannot be satisfied, their entropy will increase to the critical point that results in their collapse. In order to simulate the brittle behavior of complex system, theory of cellular automaton has been induced to describe the macro reflection of brittleness in one/complex system. Von. Neumann model is applied, which a subsystem is regarded as one cellular. The simulation rules have also been established. In a brittle basic element, brittle evaluations have been finished by employing cusp and swallow catastrophe progression methods, which brittle relation between the non-collapsed subsystems and the collapsed one ca
n be evaluated according to the brittle same degree, brittle opposite degree and brittle fluctuating degree.
Finally, on the basis of data from the Ministry of Health P.R.China from April to May, taking Beijing, and Nei Menggu as examples, brittleness research and analyses have been carried out on the S ARS based on the theory of brittleness. Then, effective methods are presented from the point of view of brittleness in order to deal with the crisis.
引文
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