Brittleness Theory Of Complex System And Its Application To Crisis Analysis

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 brittlesameness 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 can 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.